# spacegroups

hm_notation: C 1 2/c 1
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: R -3 c
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "x,x-y,1/2+z", "2/3+x,1/3+x-y,5/6+z", "1/3+x,2/3+x-y,1/6+z", "y,x,1/2-z", "2/3+y,1/3+x,5/6-z", "1/3+y,2/3+x,1/6-z", "-x+y,y,1/2+z", "2/3-x+y,1/3+y,5/6+z", "1/3-x+y,2/3+y,1/6+z", "-x,-x+y,1/2-z", "2/3-x,1/3-x+y,5/6-z", "1/3-x,2/3-x+y,1/6-z", "-y,-x,1/2+z", "2/3-y,1/3-x,5/6+z", "1/3-y,2/3-x,1/6+z", "x-y,-y,1/2-z", "2/3+x-y,1/3-y,5/6-z", "1/3+x-y,2/3-y,1/6-z", "y,-x+y,-z", "2/3+y,1/3-x+y,1/3-z", "1/3+y,2/3-x+y,2/3-z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z", "-x,-y,-z", "2/3-x,1/3-y,1/3-z", "1/3-x,2/3-y,2/3-z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "x-y,x,-z", "2/3+x-y,1/3+x,1/3-z", "1/3+x-y,2/3+x,2/3-z"]


hm_notation: F d -3 m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+z,1/2-x,1/4+y", "3/4+z,-x,3/4+y", "1/4+z,1/2-x,3/4+y", "1/4+z,-x,1/4+y", "3/4-y,1/2+z,1/4-x", "3/4-y,+z,3/4-x", "1/4-y,1/2+z,3/4-x", "1/4-y,+z,1/4-x", "3/4+x,1/2-y,1/4+z", "3/4+x,-y,3/4+z", "1/4+x,1/2-y,3/4+z", "1/4+x,-y,1/4+z", "3/4-z,1/2+x,1/4-y", "3/4-z,+x,3/4-y", "1/4-z,1/2+x,3/4-y", "1/4-z,+x,1/4-y", "3/4+y,1/2-z,1/4+x", "3/4+y,-z,3/4+x", "1/4+y,1/2-z,3/4+x", "1/4+y,-z,1/4+x", "3/4-x,1/2+y,1/4-z", "3/4-x,+y,3/4-z", "1/4-x,1/2+y,3/4-z", "1/4-x,+y,1/4-z", "1/2+x,3/4-z,1/4-y", "1/2+x,1/4-z,3/4-y", "+x,3/4-z,3/4-y", "+x,1/4-z,1/4-y", "1/2-z,3/4+y,1/4+x", "1/2-z,1/4+y,3/4+x", "-z,3/4+y,3/4+x", "-z,1/4+y,1/4+x", "1/2+y,3/4-x,1/4-z", "1/2+y,1/4-x,3/4-z", "+y,3/4-x,3/4-z", "+y,1/4-x,1/4-z", "1/2-x,3/4+z,1/4+y", "1/2-x,1/4+z,3/4+y", "-x,3/4+z,3/4+y", "-x,1/4+z,1/4+y", "1/2+z,3/4-y,1/4-x", "1/2+z,1/4-y,3/4-x", "+z,3/4-y,3/4-x", "+z,1/4-y,1/4-x", "1/2-y,3/4+x,1/4+z", "1/2-y,1/4+x,3/4+z", "-y,3/4+x,3/4+z", "-y,1/4+x,1/4+z", "x,1/2+z,1/2+y", "x,+z,+y", "1/2+x,1/2+z,+y", "1/2+x,+z,1/2+y", "-z,1/2-y,1/2-x", "-z,-y,-x", "1/2-z,1/2-y,-x", "1/2-z,-y,1/2-x", "y,1/2+x,1/2+z", "y,+x,+z", "1/2+y,1/2+x,+z", "1/2+y,+x,1/2+z", "-x,1/2-z,1/2-y", "-x,-z,-y", "1/2-x,1/2-z,-y", "1/2-x,-z,1/2-y", "z,1/2+y,1/2+x", "z,+y,+x", "1/2+z,1/2+y,+x", "1/2+z,+y,1/2+x", "-y,1/2-x,1/2-z", "-y,-x,-z", "1/2-y,1/2-x,-z", "1/2-y,-x,1/2-z", "3/4+z,1/4+x,1/2-y", "3/4+z,3/4+x,-y", "1/4+z,1/4+x,-y", "1/4+z,3/4+x,1/2-y", "3/4-y,1/4-z,1/2+x", "3/4-y,3/4-z,+x", "1/4-y,1/4-z,+x", "1/4-y,3/4-z,1/2+x", "3/4+x,1/4+y,1/2-z", "3/4+x,3/4+y,-z", "1/4+x,1/4+y,-z", "1/4+x,3/4+y,1/2-z", "3/4-z,1/4-x,1/2+y", "3/4-z,3/4-x,+y", "1/4-z,1/4-x,+y", "1/4-z,3/4-x,1/2+y", "3/4+y,1/4+z,1/2-x", "3/4+y,3/4+z,-x", "1/4+y,1/4+z,-x", "1/4+y,3/4+z,1/2-x", "3/4-x,1/4-y,1/2+z", "3/4-x,3/4-y,+z", "1/4-x,1/4-y,+z", "1/4-x,3/4-y,1/2+z", "-z,3/4+x,3/4+y", "-z,1/4+x,1/4+y", "1/2-z,3/4+x,1/4+y", "1/2-z,1/4+x,3/4+y", "y,3/4-z,3/4-x", "y,1/4-z,1/4-x", "1/2+y,3/4-z,1/4-x", "1/2+y,1/4-z,3/4-x", "-x,3/4+y,3/4+z", "-x,1/4+y,1/4+z", "1/2-x,3/4+y,1/4+z", "1/2-x,1/4+y,3/4+z", "z,3/4-x,3/4-y", "z,1/4-x,1/4-y", "1/2+z,3/4-x,1/4-y", "1/2+z,1/4-x,3/4-y", "-y,3/4+z,3/4+x", "-y,1/4+z,1/4+x", "1/2-y,3/4+z,1/4+x", "1/2-y,1/4+z,3/4+x", "x,3/4-y,3/4-z", "x,1/4-y,1/4-z", "1/2+x,3/4-y,1/4-z", "1/2+x,1/4-y,3/4-z", "1/4-x,1/2+z,3/4-y", "1/4-x,+z,1/4-y", "3/4-x,1/2+z,1/4-y", "3/4-x,+z,3/4-y", "1/4+z,1/2-y,3/4+x", "1/4+z,-y,1/4+x", "3/4+z,1/2-y,1/4+x", "3/4+z,-y,3/4+x", "1/4-y,1/2+x,3/4-z", "1/4-y,+x,1/4-z", "3/4-y,1/2+x,1/4-z", "3/4-y,+x,3/4-z", "1/4+x,1/2-z,3/4+y", "1/4+x,-z,1/4+y", "3/4+x,1/2-z,1/4+y", "3/4+x,-z,3/4+y", "1/4-z,1/2+y,3/4-x", "1/4-z,+y,1/4-x", "3/4-z,1/2+y,1/4-x", "3/4-z,+y,3/4-x", "1/4+y,1/2-x,3/4+z", "1/4+y,-x,1/4+z", "3/4+y,1/2-x,1/4+z", "3/4+y,-x,3/4+z", "3/4-x,3/4-z,y", "3/4-x,1/4-z,1/2+y", "1/4-x,3/4-z,1/2+y", "1/4-x,1/4-z,y", "3/4+z,3/4+y,-x", "3/4+z,1/4+y,1/2-x", "1/4+z,3/4+y,1/2-x", "1/4+z,1/4+y,-x", "3/4-y,3/4-x,z", "3/4-y,1/4-x,1/2+z", "1/4-y,3/4-x,1/2+z", "1/4-y,1/4-x,z", "3/4+x,3/4+z,-y", "3/4+x,1/4+z,1/2-y", "1/4+x,3/4+z,1/2-y", "1/4+x,1/4+z,-y", "3/4-z,3/4-y,x", "3/4-z,1/4-y,1/2+x", "1/4-z,3/4-y,1/2+x", "1/4-z,1/4-y,x", "3/4+y,3/4+x,-z", "3/4+y,1/4+x,1/2-z", "1/4+y,3/4+x,1/2-z", "1/4+y,1/4+x,-z", "-z,-x,-y", "-z,1/2-x,1/2-y", "1/2-z,-x,1/2-y", "1/2-z,1/2-x,-y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "-y,-z,-x", "-y,1/2-z,1/2-x", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x"]


hm_notation: P n n a
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "1/2+x,y,-z", "1/2-x,-y,z", "-x,-y,-z"]


hm_notation: P -4 3 m
symmetry_xyz:
["x,y,z", "-z,x,-y", "-y,z,-x", "-x,y,-z", "x,-z,-y", "z,-y,-x", "y,-x,-z", "x,z,y", "z,y,x", "y,x,z", "-z,-x,y", "-y,-z,x", "-x,-y,z", "z,-x,-y", "y,-z,-x", "x,-y,-z", "-x,z,-y", "-z,y,-x", "-y,x,-z", "-x,-z,y", "-z,-y,x", "-y,-x,z", "z,x,y", "y,z,x"]


hm_notation: P -6 2 m
symmetry_xyz:
["x,y,z", "-x,-x+y,z", "-x+y,-x,-z", "y,x,-z", "-y,x-y,z", "x-y,-y,z", "x,y,-z", "-x,-x+y,-z", "-x+y,-x,z", "y,x,z", "-y,x-y,-z", "x-y,-y,-z"]


hm_notation: P 4/m m m
symmetry_xyz:
["x,y,z", "-y,-x,z", "y,x,-z", "y,-x,-z", "-y,x,z", "x,-y,z", "-x,y,-z", "x,y,-z", "-x,-y,z", "y,x,z", "-y,-x,-z", "-y,x,-z", "y,-x,z", "-x,y,z", "x,-y,-z", "-x,-y,-z"]


hm_notation: C 1 2/m 1
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: P n m a
symmetry_xyz:
["x,y,z", "x,1/2-y,z", "-x,1/2+y,-z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "1/2+x,y,1/2-z", "1/2-x,-y,1/2+z", "-x,-y,-z"]


hm_notation: P -4 3 n
symmetry_xyz:
["x,y,z", "-z,x,-y", "-y,z,-x", "-x,y,-z", "1/2+x,1/2-z,1/2-y", "1/2+z,1/2-y,1/2-x", "1/2+y,1/2-x,1/2-z", "1/2+x,1/2+z,1/2+y", "1/2+z,1/2+y,1/2+x", "1/2+y,1/2+x,1/2+z", "-z,-x,y", "-y,-z,x", "-x,-y,z", "z,-x,-y", "y,-z,-x", "x,-y,-z", "1/2-x,1/2+z,1/2-y", "1/2-z,1/2+y,1/2-x", "1/2-y,1/2+x,1/2-z", "1/2-x,1/2-z,1/2+y", "1/2-z,1/2-y,1/2+x", "1/2-y,1/2-x,1/2+z", "z,x,y", "y,z,x"]


hm_notation: P b c m
symmetry_xyz:
["x,y,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "-x,1/2+y,z", "x,1/2-y,-z", "x,y,1/2-z", "-x,-y,1/2+z", "-x,-y,-z"]


hm_notation: P n a m
symmetry_xyz:
["x,y,z", "x,y,1/2-z", "-x,-y,1/2+z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "-x,-y,-z"]


hm_notation: I -4 3 d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-z,x,-y", "-z,1/2+x,1/2-y", "1/2-y,z,-x", "-y,1/2+z,1/2-x", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "1/4+x,3/4-z,1/4-y", "3/4+x,1/4-z,3/4-y", "1/4+z,3/4-y,1/4-x", "3/4+z,1/4-y,3/4-x", "1/4+y,3/4-x,1/4-z", "3/4+y,1/4-x,3/4-z", "1/4+x,1/4+z,1/4+y", "3/4+x,3/4+z,3/4+y", "1/4+z,1/4+y,1/4+x", "3/4+z,3/4+y,3/4+x", "1/4+y,1/4+x,1/4+z", "3/4+y,3/4+x,3/4+z", "-z,1/2-x,y", "1/2-z,-x,1/2+y", "-y,1/2-z,x", "1/2-y,-z,1/2+x", "-x,1/2-y,z", "1/2-x,-y,1/2+z", "1/2+z,1/2-x,-y", "+z,-x,1/2-y", "1/2+y,1/2-z,-x", "+y,-z,1/2-x", "1/2+x,1/2-y,-z", "+x,-y,1/2-z", "3/4-x,3/4+z,1/4-y", "1/4-x,1/4+z,3/4-y", "3/4-z,3/4+y,1/4-x", "1/4-z,1/4+y,3/4-x", "3/4-y,3/4+x,1/4-z", "1/4-y,1/4+x,3/4-z", "3/4-x,1/4-z,1/4+y", "1/4-x,3/4-z,3/4+y", "3/4-z,1/4-y,1/4+x", "1/4-z,3/4-y,3/4+x", "3/4-y,1/4-x,1/4+z", "1/4-y,3/4-x,3/4+z", "z,x,y", "1/2+z,1/2+x,1/2+y", "y,z,x", "1/2+y,1/2+z,1/2+x"]


hm_notation: I -4
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-y,x,-z", "1/2-y,1/2+x,1/2-z"]


hm_notation: R -3 m
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "x,x-y,z", "2/3+x,1/3+x-y,1/3+z", "1/3+x,2/3+x-y,2/3+z", "y,x,-z", "2/3+y,1/3+x,1/3-z", "1/3+y,2/3+x,2/3-z", "-x+y,y,z", "2/3-x+y,1/3+y,1/3+z", "1/3-x+y,2/3+y,2/3+z", "-x,-x+y,-z", "2/3-x,1/3-x+y,1/3-z", "1/3-x,2/3-x+y,2/3-z", "-y,-x,z", "2/3-y,1/3-x,1/3+z", "1/3-y,2/3-x,2/3+z", "x-y,-y,-z", "2/3+x-y,1/3-y,1/3-z", "1/3+x-y,2/3-y,2/3-z", "y,-x+y,-z", "2/3+y,1/3-x+y,1/3-z", "1/3+y,2/3-x+y,2/3-z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z", "-x,-y,-z", "2/3-x,1/3-y,1/3-z", "1/3-x,2/3-y,2/3-z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "x-y,x,-z", "2/3+x-y,1/3+x,1/3-z", "1/3+x-y,2/3+x,2/3-z"]


hm_notation: P -3 1 c
symmetry_xyz:
["x,y,z", "x-y,-y,1/2+z", "y,-x+y,-z", "-y,-x,1/2-z", "-x+y,-x,z", "-x,-x+y,1/2+z", "-x,-y,-z", "-x+y,y,1/2-z", "-y,x-y,z", "y,x,1/2+z", "x-y,x,-z", "x,x-y,1/2-z"]


hm_notation: P 63 m c
symmetry_xyz:
["x,y,z", "-x,-x+y,1/2+z", "x-y,x,1/2+z", "-y,-x,z", "-y,x-y,z", "x-y,-y,1/2+z", "-x,-y,1/2+z", "x,x-y,z", "-x+y,-x,z", "y,x,1/2+z", "y,-x+y,1/2+z", "-x+y,y,z"]


hm_notation: A m a m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,-y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,y,-z", "x,1/2+y,1/2-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,y,z", "1/2-x,1/2+y,1/2+z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P n m n
symmetry_xyz:
["x,y,z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "x,-y,z", "-x,y,-z", "-x,-y,-z"]


hm_notation: F m 3 m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "z,-x,y", "z,1/2-x,1/2+y", "1/2+z,-x,1/2+y", "1/2+z,1/2-x,y", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "y,-z,x", "y,1/2-z,1/2+x", "1/2+y,-z,1/2+x", "1/2+y,1/2-z,x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-z,-y", "x,1/2-z,1/2-y", "1/2+x,-z,1/2-y", "1/2+x,1/2-z,-y", "-z,y,x", "-z,1/2+y,1/2+x", "1/2-z,y,1/2+x", "1/2-z,1/2+y,x", "y,-x,-z", "y,1/2-x,1/2-z", "1/2+y,-x,1/2-z", "1/2+y,1/2-x,-z", "-x,z,y", "-x,1/2+z,1/2+y", "1/2-x,z,1/2+y", "1/2-x,1/2+z,y", "z,-y,-x", "z,1/2-y,1/2-x", "1/2+z,-y,1/2-x", "1/2+z,1/2-y,-x", "-y,x,z", "-y,1/2+x,1/2+z", "1/2-y,x,1/2+z", "1/2-y,1/2+x,z", "x,z,y", "x,1/2+z,1/2+y", "1/2+x,z,1/2+y", "1/2+x,1/2+z,y", "-z,-y,-x", "-z,1/2-y,1/2-x", "1/2-z,-y,1/2-x", "1/2-z,1/2-y,-x", "y,x,z", "y,1/2+x,1/2+z", "1/2+y,x,1/2+z", "1/2+y,1/2+x,z", "-x,-z,-y", "-x,1/2-z,1/2-y", "1/2-x,-z,1/2-y", "1/2-x,1/2-z,-y", "z,y,x", "z,1/2+y,1/2+x", "1/2+z,y,1/2+x", "1/2+z,1/2+y,x", "-y,-x,-z", "-y,1/2-x,1/2-z", "1/2-y,-x,1/2-z", "1/2-y,1/2-x,-z", "z,x,-y", "z,1/2+x,1/2-y", "1/2+z,x,1/2-y", "1/2+z,1/2+x,-y", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "y,z,-x", "y,1/2+z,1/2-x", "1/2+y,z,1/2-x", "1/2+y,1/2+z,-x", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "-z,x,y", "-z,1/2+x,1/2+y", "1/2-z,x,1/2+y", "1/2-z,1/2+x,y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "-y,z,x", "-y,1/2+z,1/2+x", "1/2-y,z,1/2+x", "1/2-y,1/2+z,x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,z,-y", "-x,1/2+z,1/2-y", "1/2-x,z,1/2-y", "1/2-x,1/2+z,-y", "z,-y,x", "z,1/2-y,1/2+x", "1/2+z,-y,1/2+x", "1/2+z,1/2-y,x", "-y,x,-z", "-y,1/2+x,1/2-z", "1/2-y,x,1/2-z", "1/2-y,1/2+x,-z", "x,-z,y", "x,1/2-z,1/2+y", "1/2+x,-z,1/2+y", "1/2+x,1/2-z,y", "-z,y,-x", "-z,1/2+y,1/2-x", "1/2-z,y,1/2-x", "1/2-z,1/2+y,-x", "y,-x,z", "y,1/2-x,1/2+z", "1/2+y,-x,1/2+z", "1/2+y,1/2-x,z", "-x,-z,y", "-x,1/2-z,1/2+y", "1/2-x,-z,1/2+y", "1/2-x,1/2-z,y", "z,y,-x", "z,1/2+y,1/2-x", "1/2+z,y,1/2-x", "1/2+z,1/2+y,-x", "-y,-x,z", "-y,1/2-x,1/2+z", "1/2-y,-x,1/2+z", "1/2-y,1/2-x,z", "x,z,-y", "x,1/2+z,1/2-y", "1/2+x,z,1/2-y", "1/2+x,1/2+z,-y", "-z,-y,x", "-z,1/2-y,1/2+x", "1/2-z,-y,1/2+x", "1/2-z,1/2-y,x", "y,x,-z", "y,1/2+x,1/2-z", "1/2+y,x,1/2-z", "1/2+y,1/2+x,-z", "-z,-x,-y", "-z,1/2-x,1/2-y", "1/2-z,-x,1/2-y", "1/2-z,1/2-x,-y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "-y,-z,-x", "-y,1/2-z,1/2-x", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x"]


hm_notation: C 2 2 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "x,-y,-z", "1/2+x,1/2-y,-z", "-x,-y,z", "1/2-x,1/2-y,z"]


hm_notation: F d d d
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+x,-y,3/4+z", "3/4+x,1/2-y,1/4+z", "1/4+x,-y,1/4+z", "1/4+x,1/2-y,3/4+z", "3/4-x,y,3/4-z", "3/4-x,1/2+y,1/4-z", "1/4-x,y,1/4-z", "1/4-x,1/2+y,3/4-z", "-x,3/4+y,3/4+z", "-x,1/4+y,1/4+z", "1/2-x,3/4+y,1/4+z", "1/2-x,1/4+y,3/4+z", "x,3/4-y,3/4-z", "x,1/4-y,1/4-z", "1/2+x,3/4-y,1/4-z", "1/2+x,1/4-y,3/4-z", "3/4+x,3/4+y,-z", "3/4+x,1/4+y,1/2-z", "1/4+x,3/4+y,1/2-z", "1/4+x,1/4+y,-z", "3/4-x,3/4-y,z", "3/4-x,1/4-y,1/2+z", "1/4-x,3/4-y,1/2+z", "1/4-x,1/4-y,z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: R 3 2
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "-x,-x+y,-z", "2/3-x,1/3-x+y,1/3-z", "1/3-x,2/3-x+y,2/3-z", "y,x,-z", "2/3+y,1/3+x,1/3-z", "1/3+y,2/3+x,2/3-z", "x-y,-y,-z", "2/3+x-y,1/3-y,1/3-z", "1/3+x-y,2/3-y,2/3-z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z"]


hm_notation: P c a m
symmetry_xyz:
["x,y,z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "1/2+x,-y,z", "1/2-x,y,-z", "x,y,1/2-z", "-x,-y,1/2+z", "-x,-y,-z"]


hm_notation: P b n m
symmetry_xyz:
["x,y,z", "x,y,1/2-z", "-x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "-x,-y,-z"]


hm_notation: P -4 21 c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "y,-x,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "-y,x,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: P 41 21 2
symmetry_xyz:
["x,y,z", "y,x,-z", "1/2-y,1/2+x,1/4+z", "1/2-x,1/2+y,1/4-z", "-x,-y,1/2+z", "-y,-x,1/2-z", "1/2+y,1/2-x,3/4+z", "1/2+x,1/2-y,3/4-z"]


hm_notation: P m n n
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "-x,y,z", "x,-y,-z", "-x,-y,-z"]


hm_notation: I m m a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2-y,z", "1/2+x,-y,1/2+z", "-x,1/2+y,-z", "1/2-x,+y,1/2-z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "-x,1/2-y,z", "1/2-x,-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: C m c 21
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,z", "1/2-x,1/2+y,z", "-x,-y,1/2+z", "1/2-x,1/2-y,1/2+z"]


hm_notation: R -3 %var1%
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "y,-x+y,-z", "2/3+y,1/3-x+y,1/3-z", "1/3+y,2/3-x+y,2/3-z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z", "-x,-y,-z", "2/3-x,1/3-y,1/3-z", "1/3-x,2/3-y,2/3-z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "x-y,x,-z", "2/3+x-y,1/3+x,1/3-z", "1/3+x-y,2/3+x,2/3-z"]


hm_notation: P a 3
symmetry_xyz:
["x,y,z", "1/2+z,x,1/2-y", "z,1/2-x,1/2+y", "1/2-z,1/2+x,y", "-z,-x,-y", "1/2+y,1/2-z,-x", "1/2-y,-z,1/2+x", "-y,1/2+z,1/2-x", "y,z,x", "x,1/2-y,1/2+z", "1/2-x,1/2+y,z", "1/2+x,y,1/2-z", "-x,-y,-z", "1/2-z,-x,1/2+y", "-z,1/2+x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "1/2-y,1/2+z,x", "1/2+y,z,1/2-x", "y,1/2-z,1/2+x", "-y,-z,-x", "-x,1/2+y,1/2-z", "1/2+x,1/2-y,-z", "1/2-x,-y,1/2+z"]


hm_notation: P b c n
symmetry_xyz:
["x,y,z", "x,-y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z"]


hm_notation: I 4/m m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,-x,z", "1/2-y,1/2-x,1/2+z", "y,x,-z", "1/2+y,1/2+x,1/2-z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "y,x,z", "1/2+y,1/2+x,1/2+z", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "y,-x,z", "1/2+y,1/2-x,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P 6/m c c
symmetry_xyz:
["x,y,z", "-x,-x+y,1/2+z", "x,x-y,1/2-z", "-x+y,-x,-z", "x-y,x,z", "-y,-x,1/2+z", "y,x,1/2-z", "y,-x+y,-z", "-y,x-y,z", "x-y,-y,1/2+z", "-x+y,y,1/2-z", "x,y,-z", "-x,-y,z", "x,x-y,1/2+z", "-x,-x+y,1/2-z", "x-y,x,-z", "-x+y,-x,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,x-y,-z", "y,-x+y,z", "-x+y,y,1/2+z", "x-y,-y,1/2-z", "-x,-y,-z"]


hm_notation: P -3 m 1
symmetry_xyz:
["x,y,z", "-y,-x,z", "y,-x+y,-z", "-x,-x+y,-z", "-x+y,-x,z", "-x+y,y,z", "-x,-y,-z", "y,x,-z", "-y,x-y,z", "x,x-y,z", "x-y,x,-z", "x-y,-y,-z"]


hm_notation: I 1 2/m 1
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: F -4 3 c
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-z,1/2-y", "x,1/2-z,-y", "1/2+x,-z,-y", "1/2+x,1/2-z,1/2-y", "z,-y,1/2-x", "z,1/2-y,-x", "1/2+z,-y,-x", "1/2+z,1/2-y,1/2-x", "y,-x,1/2-z", "y,1/2-x,-z", "1/2+y,-x,-z", "1/2+y,1/2-x,1/2-z", "x,z,1/2+y", "x,1/2+z,+y", "1/2+x,z,+y", "1/2+x,1/2+z,1/2+y", "z,y,1/2+x", "z,1/2+y,+x", "1/2+z,y,+x", "1/2+z,1/2+y,1/2+x", "y,x,1/2+z", "y,1/2+x,+z", "1/2+y,x,+z", "1/2+y,1/2+x,1/2+z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,z,1/2-y", "-x,1/2+z,-y", "1/2-x,z,-y", "1/2-x,1/2+z,1/2-y", "-z,y,1/2-x", "-z,1/2+y,-x", "1/2-z,y,-x", "1/2-z,1/2+y,1/2-x", "-y,x,1/2-z", "-y,1/2+x,-z", "1/2-y,x,-z", "1/2-y,1/2+x,1/2-z", "-x,-z,1/2+y", "-x,1/2-z,+y", "1/2-x,-z,+y", "1/2-x,1/2-z,1/2+y", "-z,-y,1/2+x", "-z,1/2-y,+x", "1/2-z,-y,+x", "1/2-z,1/2-y,1/2+x", "-y,-x,1/2+z", "-y,1/2-x,+z", "1/2-y,-x,+z", "1/2-y,1/2-x,1/2+z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x"]


hm_notation: P c c n
symmetry_xyz:
["x,y,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-x,-y,-z"]


hm_notation: P m 3 m
symmetry_xyz:
["x,y,z", "z,-x,y", "-y,z,-x", "x,-y,z", "-z,x,-y", "y,-z,x", "-x,y,-z", "x,-z,-y", "-z,y,x", "y,-x,-z", "-x,z,y", "z,-y,-x", "-y,x,z", "x,z,y", "-z,-y,-x", "y,x,z", "-x,-z,-y", "z,y,x", "-y,-x,-z", "z,x,-y", "-y,-z,x", "x,y,-z", "-z,-x,y", "y,z,-x", "-x,-y,z", "-z,x,y", "y,-z,-x", "-x,y,z", "z,-x,-y", "-y,z,x", "x,-y,-z", "-x,z,-y", "z,-y,x", "-y,x,-z", "x,-z,y", "-z,y,-x", "y,-x,z", "-x,-z,y", "z,y,-x", "-y,-x,z", "x,z,-y", "-z,-y,x", "y,x,-z", "-z,-x,-y", "y,z,x", "-x,-y,-z", "z,x,y", "-y,-z,-x"]


hm_notation: P c m n
symmetry_xyz:
["x,y,z", "x,1/2-y,z", "-x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "-x,-y,-z"]


hm_notation: P 63/m m c
symmetry_xyz:
["x,y,z", "-x,-x+y,1/2+z", "x,x-y,1/2-z", "-x+y,-x,1/2-z", "x-y,x,1/2+z", "-y,-x,z", "y,x,-z", "y,-x+y,-z", "-y,x-y,z", "x-y,-y,1/2+z", "-x+y,y,1/2-z", "x,y,1/2-z", "-x,-y,1/2+z", "x,x-y,z", "-x,-x+y,-z", "x-y,x,-z", "-x+y,-x,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,x-y,1/2-z", "y,-x+y,1/2+z", "-x+y,y,z", "x-y,-y,-z", "-x,-y,-z"]


hm_notation: I 1 2/c 1
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 41/a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "3/4+y,1/4-x,1/4-z", "1/4+y,3/4-x,3/4-z", "3/4-y,1/4+x,1/4+z", "1/4-y,3/4+x,3/4+z", "1/2+x,y,1/2-z", "+x,1/2+y,-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "3/4-y,3/4+x,3/4-z", "1/4-y,1/4+x,1/4-z", "3/4+y,3/4-x,3/4+z", "1/4+y,1/4-x,1/4+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 4/m c m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,-x,1/2+z", "1/2-y,1/2-x,+z", "y,x,1/2-z", "1/2+y,1/2+x,-z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "y,x,1/2+z", "1/2+y,1/2+x,+z", "-y,-x,1/2-z", "1/2-y,1/2-x,-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "y,-x,z", "1/2+y,1/2-x,1/2+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: A c a m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,1/2-y,z", "1/2+x,-y,1/2+z", "1/2-x,1/2+y,-z", "1/2-x,+y,1/2-z", "x,y,-z", "x,1/2+y,1/2-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,1/2+y,z", "1/2-x,+y,1/2+z", "1/2+x,1/2-y,-z", "1/2+x,-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: I 41/a m d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/4-y,3/4-x,1/4+z", "3/4-y,1/4-x,3/4+z", "1/4+y,3/4+x,1/4-z", "3/4+y,1/4+x,3/4-z", "1/4+y,3/4-x,1/4-z", "3/4+y,1/4-x,3/4-z", "1/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/2+x,-y,1/2+z", "+x,1/2-y,+z", "1/2-x,y,1/2-z", "-x,1/2+y,-z", "1/2+x,y,1/2-z", "+x,1/2+y,-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "1/4+y,1/4+x,3/4+z", "3/4+y,3/4+x,1/4+z", "1/4-y,1/4-x,3/4-z", "3/4-y,3/4-x,1/4-z", "1/4-y,1/4+x,3/4-z", "3/4-y,3/4+x,1/4-z", "1/4+y,1/4-x,3/4+z", "3/4+y,3/4-x,1/4+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P n c n
symmetry_xyz:
["x,y,z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "x,-y,1/2+z", "-x,y,1/2-z", "-x,-y,-z"]


hm_notation: C m c a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,+y,1/2-z", "-x,y,z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2+x,1/2-y,-z", "x,1/2+y,1/2-z", "1/2+x,+y,1/2-z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: C c c m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,1/2-z", "-x,y,1/2+z", "1/2-x,1/2+y,1/2+z", "x,-y,1/2-z", "1/2+x,1/2-y,1/2-z", "x,y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2-x,1/2-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: F m 3 c
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "z,-x,y", "z,1/2-x,1/2+y", "1/2+z,-x,1/2+y", "1/2+z,1/2-x,y", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "y,-z,x", "y,1/2-z,1/2+x", "1/2+y,-z,1/2+x", "1/2+y,1/2-z,x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-z,1/2-y", "x,1/2-z,-y", "1/2+x,-z,-y", "1/2+x,1/2-z,1/2-y", "-z,y,1/2+x", "-z,1/2+y,+x", "1/2-z,y,+x", "1/2-z,1/2+y,1/2+x", "y,-x,1/2-z", "y,1/2-x,-z", "1/2+y,-x,-z", "1/2+y,1/2-x,1/2-z", "-x,z,1/2+y", "-x,1/2+z,+y", "1/2-x,z,+y", "1/2-x,1/2+z,1/2+y", "z,-y,1/2-x", "z,1/2-y,-x", "1/2+z,-y,-x", "1/2+z,1/2-y,1/2-x", "-y,x,1/2+z", "-y,1/2+x,+z", "1/2-y,x,+z", "1/2-y,1/2+x,1/2+z", "x,z,1/2+y", "x,1/2+z,+y", "1/2+x,z,+y", "1/2+x,1/2+z,1/2+y", "-z,-y,1/2-x", "-z,1/2-y,-x", "1/2-z,-y,-x", "1/2-z,1/2-y,1/2-x", "y,x,1/2+z", "y,1/2+x,+z", "1/2+y,x,+z", "1/2+y,1/2+x,1/2+z", "-x,-z,1/2-y", "-x,1/2-z,-y", "1/2-x,-z,-y", "1/2-x,1/2-z,1/2-y", "z,y,1/2+x", "z,1/2+y,+x", "1/2+z,y,+x", "1/2+z,1/2+y,1/2+x", "-y,-x,1/2-z", "-y,1/2-x,-z", "1/2-y,-x,-z", "1/2-y,1/2-x,1/2-z", "z,x,-y", "z,1/2+x,1/2-y", "1/2+z,x,1/2-y", "1/2+z,1/2+x,-y", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "y,z,-x", "y,1/2+z,1/2-x", "1/2+y,z,1/2-x", "1/2+y,1/2+z,-x", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "-z,x,y", "-z,1/2+x,1/2+y", "1/2-z,x,1/2+y", "1/2-z,1/2+x,y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "-y,z,x", "-y,1/2+z,1/2+x", "1/2-y,z,1/2+x", "1/2-y,1/2+z,x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,z,1/2-y", "-x,1/2+z,-y", "1/2-x,z,-y", "1/2-x,1/2+z,1/2-y", "z,-y,1/2+x", "z,1/2-y,+x", "1/2+z,-y,+x", "1/2+z,1/2-y,1/2+x", "-y,x,1/2-z", "-y,1/2+x,-z", "1/2-y,x,-z", "1/2-y,1/2+x,1/2-z", "x,-z,1/2+y", "x,1/2-z,+y", "1/2+x,-z,+y", "1/2+x,1/2-z,1/2+y", "-z,y,1/2-x", "-z,1/2+y,-x", "1/2-z,y,-x", "1/2-z,1/2+y,1/2-x", "y,-x,1/2+z", "y,1/2-x,+z", "1/2+y,-x,+z", "1/2+y,1/2-x,1/2+z", "-x,-z,1/2+y", "-x,1/2-z,+y", "1/2-x,-z,+y", "1/2-x,1/2-z,1/2+y", "z,y,1/2-x", "z,1/2+y,-x", "1/2+z,y,-x", "1/2+z,1/2+y,1/2-x", "-y,-x,1/2+z", "-y,1/2-x,+z", "1/2-y,-x,+z", "1/2-y,1/2-x,1/2+z", "x,z,1/2-y", "x,1/2+z,-y", "1/2+x,z,-y", "1/2+x,1/2+z,1/2-y", "-z,-y,1/2+x", "-z,1/2-y,+x", "1/2-z,-y,+x", "1/2-z,1/2-y,1/2+x", "y,x,1/2-z", "y,1/2+x,-z", "1/2+y,x,-z", "1/2+y,1/2+x,1/2-z", "-z,-x,-y", "-z,1/2-x,1/2-y", "1/2-z,-x,1/2-y", "1/2-z,1/2-x,-y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "-y,-z,-x", "-y,1/2-z,1/2-x", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x"]


hm_notation: C m c m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,1/2-z", "-x,y,z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2+x,1/2-y,-z", "x,y,1/2-z", "1/2+x,1/2+y,1/2-z", "-x,-y,1/2+z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: P 4/n m m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "y,x,-z", "y,-x,-z", "1/2-y,1/2+x,z", "x,-y,z", "1/2-x,1/2+y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2+y,1/2+x,z", "-y,-x,-z", "-y,x,-z", "1/2+y,1/2-x,z", "-x,y,z", "1/2+x,1/2-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: C c c a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,-z", "-x,1/2+y,1/2+z", "1/2-x,+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,-z", "x,1/2+y,1/2-z", "1/2+x,+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z"]


hm_notation: P c c a
symmetry_xyz:
["x,y,z", "x,-y,1/2+z", "-x,y,1/2-z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "1/2+x,y,-z", "1/2-x,-y,z", "-x,-y,-z"]


hm_notation: P 63/m
symmetry_xyz:
["x,y,z", "-x+y,-x,1/2-z", "x-y,x,1/2+z", "y,-x+y,-z", "-y,x-y,z", "x,y,1/2-z", "-x,-y,1/2+z", "x-y,x,-z", "-x+y,-x,z", "-y,x-y,1/2-z", "y,-x+y,1/2+z", "-x,-y,-z"]


hm_notation: B 2 m b
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "x,1/2-y,z", "1/2+x,1/2-y,1/2+z", "x,-y,-z", "1/2+x,-y,1/2-z"]


hm_notation: I 41/a %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/4+y,3/4-x,1/4-z", "3/4+y,1/4-x,3/4-z", "1/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/2+x,y,1/2-z", "+x,1/2+y,-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "1/4-y,1/4+x,3/4-z", "3/4-y,3/4+x,1/4-z", "1/4+y,1/4-x,3/4+z", "3/4+y,3/4-x,1/4+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P m c n
symmetry_xyz:
["x,y,z", "1/2-x,y,z", "1/2+x,-y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "-x,-y,-z"]


hm_notation: P b c a
symmetry_xyz:
["x,y,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "1/2+x,y,1/2-z", "1/2-x,-y,1/2+z", "-x,-y,-z"]


hm_notation: I 4/m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "y,-x,z", "1/2+y,1/2-x,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 1 2/a 1
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P 63/m c m
symmetry_xyz:
["x,y,z", "-x,-x+y,z", "x,x-y,-z", "-x+y,-x,1/2-z", "x-y,x,1/2+z", "-y,-x,1/2+z", "y,x,1/2-z", "y,-x+y,-z", "-y,x-y,z", "x-y,-y,z", "-x+y,y,-z", "x,y,1/2-z", "-x,-y,1/2+z", "x,x-y,1/2+z", "-x,-x+y,1/2-z", "x-y,x,-z", "-x+y,-x,z", "y,x,z", "-y,-x,-z", "-y,x-y,1/2-z", "y,-x+y,1/2+z", "-x+y,y,1/2+z", "x-y,-y,1/2-z", "-x,-y,-z"]


hm_notation: P 21 3
symmetry_xyz:
["x,y,z", "1/2-z,-x,1/2+y", "-z,1/2+x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "1/2+y,1/2-z,-x", "1/2-y,-z,1/2+x", "-y,1/2+z,1/2-x", "y,z,x", "-x,1/2+y,1/2-z", "1/2+x,1/2-y,-z", "1/2-x,-y,1/2+z"]


hm_notation: P 4 b m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "-y,x,z", "1/2+x,1/2-y,z", "-x,-y,z", "1/2+y,1/2+x,z", "y,-x,z", "1/2-x,1/2+y,z"]


hm_notation: R 3 c
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "x,x-y,1/2+z", "2/3+x,1/3+x-y,5/6+z", "1/3+x,2/3+x-y,1/6+z", "-y,-x,1/2+z", "2/3-y,1/3-x,5/6+z", "1/3-y,2/3-x,1/6+z", "-x+y,y,1/2+z", "2/3-x+y,1/3+y,5/6+z", "1/3-x+y,2/3+y,1/6+z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z"]


hm_notation: I 41/a c d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,1/2-x,3/4+z", "1/2-y,-x,1/4+z", "1/2+y,1/2+x,-z", "+y,+x,1/2-z", "1/2+y,1/2-x,1/2-z", "+y,-x,-z", "-y,1/2+x,1/4+z", "1/2-y,+x,3/4+z", "1/2+x,1/2-y,z", "+x,-y,1/2+z", "1/2-x,y,1/4-z", "-x,1/2+y,3/4-z", "1/2+x,y,3/4-z", "+x,1/2+y,1/4-z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z", "1/2+y,x,1/4+z", "+y,1/2+x,3/4+z", "-y,-x,1/2-z", "1/2-y,1/2-x,-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "1/2+y,-x,3/4+z", "+y,1/2-x,1/4+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,1/2-y,3/4-z", "1/2+x,-y,1/4-z", "-x,1/2-y,1/4-z", "1/2-x,-y,3/4-z"]


hm_notation: I a 3 d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "z,1/2-x,1/2+y", "1/2+z,-x,+y", "-y,1/2+z,1/2-x", "1/2-y,+z,-x", "x,1/2-y,1/2+z", "1/2+x,-y,+z", "-z,1/2+x,1/2-y", "1/2-z,+x,-y", "y,1/2-z,1/2+x", "1/2+y,-z,+x", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "3/4+x,1/4-z,3/4-y", "1/4+x,3/4-z,1/4-y", "3/4-z,1/4+y,3/4+x", "1/4-z,3/4+y,1/4+x", "3/4+y,1/4-x,3/4-z", "1/4+y,3/4-x,1/4-z", "3/4-x,1/4+z,3/4+y", "1/4-x,3/4+z,1/4+y", "3/4+z,1/4-y,3/4-x", "1/4+z,3/4-y,1/4-x", "3/4-y,1/4+x,3/4+z", "1/4-y,3/4+x,1/4+z", "1/4+x,1/4+z,1/4+y", "3/4+x,3/4+z,3/4+y", "1/4-z,1/4-y,1/4-x", "3/4-z,3/4-y,3/4-x", "1/4+y,1/4+x,1/4+z", "3/4+y,3/4+x,3/4+z", "1/4-x,1/4-z,1/4-y", "3/4-x,3/4-z,3/4-y", "1/4+z,1/4+y,1/4+x", "3/4+z,3/4+y,3/4+x", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,3/4-z", "1/2+z,x,1/2-y", "+z,1/2+x,-y", "1/2-y,-z,1/2+x", "-y,1/2-z,+x", "1/2+x,y,1/2-z", "+x,1/2+y,-z", "1/2-z,-x,1/2+y", "-z,1/2-x,+y", "1/2+y,z,1/2-x", "+y,1/2+z,-x", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "1/2-z,1/2+x,y", "-z,+x,1/2+y", "1/2+y,1/2-z,-x", "+y,-z,1/2-x", "1/2-x,1/2+y,z", "-x,+y,1/2+z", "1/2+z,1/2-x,-y", "+z,-x,1/2-y", "1/2-y,1/2+z,x", "-y,+z,1/2+x", "1/2+x,1/2-y,-z", "+x,-y,1/2-z", "3/4-x,3/4+z,1/4-y", "1/4-x,1/4+z,3/4-y", "3/4+z,3/4-y,1/4+x", "1/4+z,1/4-y,3/4+x", "3/4-y,3/4+x,1/4-z", "1/4-y,1/4+x,3/4-z", "3/4+x,3/4-z,1/4+y", "1/4+x,1/4-z,3/4+y", "3/4-z,3/4+y,1/4-x", "1/4-z,1/4+y,3/4-x", "3/4+y,3/4-x,1/4+z", "1/4+y,1/4-x,3/4+z", "1/4-x,3/4-z,3/4+y", "3/4-x,1/4-z,1/4+y", "1/4+z,3/4+y,3/4-x", "3/4+z,1/4+y,1/4-x", "1/4-y,3/4-x,3/4+z", "3/4-y,1/4-x,1/4+z", "1/4+x,3/4+z,3/4-y", "3/4+x,1/4+z,1/4-y", "1/4-z,3/4-y,3/4+x", "3/4-z,1/4-y,1/4+x", "1/4+y,3/4+x,3/4-z", "3/4+y,1/4+x,1/4-z", "-z,-x,-y", "1/2-z,1/2-x,1/2-y", "y,z,x", "1/2+y,1/2+z,1/2+x", "-x,-y,-z", "1/2-x,1/2-y,1/2-z", "z,x,y", "1/2+z,1/2+x,1/2+y", "-y,-z,-x", "1/2-y,1/2-z,1/2-x"]


hm_notation: P n c a
symmetry_xyz:
["x,y,z", "1/2+x,y,-z", "1/2-x,-y,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: P -3 1 m
symmetry_xyz:
["x,y,z", "x-y,-y,z", "y,-x+y,-z", "-y,-x,-z", "-x+y,-x,z", "-x,-x+y,z", "-x,-y,-z", "-x+y,y,-z", "-y,x-y,z", "y,x,z", "x-y,x,-z", "x,x-y,-z"]


hm_notation: P -3 c 1
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "y,-x+y,-z", "-x,-x+y,1/2-z", "-x+y,-x,z", "-x+y,y,1/2+z", "-x,-y,-z", "y,x,1/2-z", "-y,x-y,z", "x,x-y,1/2+z", "x-y,x,-z", "x-y,-y,1/2-z"]


hm_notation: P 63 c m
symmetry_xyz:
["x,y,z", "-x,-x+y,z", "x-y,x,1/2+z", "-y,-x,1/2+z", "-y,x-y,z", "x-y,-y,z", "-x,-y,1/2+z", "x,x-y,1/2+z", "-x+y,-x,z", "y,x,z", "y,-x+y,1/2+z", "-x+y,y,1/2+z"]


hm_notation: P 4/n m m %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "1/2+y,1/2+x,-z", "1/2+y,-x,-z", "1/2-y,x,z", "x,1/2-y,z", "-x,1/2+y,-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "y,x,z", "-y,-x,-z", "-y,1/2+x,-z", "y,1/2-x,z", "1/2-x,y,z", "1/2+x,-y,-z", "-x,-y,-z"]


hm_notation: P n n m
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "x,y,-z", "-x,-y,z", "-x,-y,-z"]


hm_notation: P -4 21 m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "y,-x,-z", "1/2-x,1/2+y,-z", "-x,-y,z", "1/2+y,1/2+x,z", "-y,x,-z", "1/2+x,1/2-y,-z"]


hm_notation: R 3 m
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "x,x-y,z", "2/3+x,1/3+x-y,1/3+z", "1/3+x,2/3+x-y,2/3+z", "-y,-x,z", "2/3-y,1/3-x,1/3+z", "1/3-y,2/3-x,2/3+z", "-x+y,y,z", "2/3-x+y,1/3+y,1/3+z", "1/3-x+y,2/3+y,2/3+z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z"]


hm_notation: P -6 c 2
symmetry_xyz:
["x,y,z", "x,x-y,-z", "-x+y,-x,1/2-z", "-y,-x,1/2+z", "-y,x-y,z", "-x+y,y,-z", "x,y,1/2-z", "x,x-y,1/2+z", "-x+y,-x,z", "-y,-x,-z", "-y,x-y,1/2-z", "-x+y,y,1/2+z"]


hm_notation: P -6 m 2
symmetry_xyz:
["x,y,z", "x,x-y,-z", "-x+y,-x,-z", "-y,-x,z", "-y,x-y,z", "-x+y,y,-z", "x,y,-z", "x,x-y,z", "-x+y,-x,z", "-y,-x,-z", "-y,x-y,-z", "-x+y,y,z"]


hm_notation: I -4 2 d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-y,-x,3/4+z", "-y,1/2-x,1/4+z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-x,1/2+y,1/4-z", "1/2-x,+y,3/4-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "1/2+y,x,3/4+z", "+y,1/2+x,1/4+z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "x,1/2-y,1/4-z", "1/2+x,-y,3/4-z"]


hm_notation: P 4/n n c
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "y,x,1/2-z", "1/2+y,-x,-z", "1/2-y,x,z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "1/2+y,1/2+x,1/2+z", "1/2-y,1/2-x,1/2-z", "-y,1/2+x,-z", "y,1/2-x,z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: F d 3
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+z,1/4+x,-y", "1/4+z,3/4+x,1/2-y", "3/4+z,1/4+x,1/2-y", "3/4+z,3/4+x,-y", "1/4+z,-x,1/4+y", "1/4+z,1/2-x,3/4+y", "3/4+z,-x,3/4+y", "3/4+z,1/2-x,1/4+y", "-z,1/4+x,1/4+y", "-z,3/4+x,3/4+y", "1/2-z,1/4+x,3/4+y", "1/2-z,3/4+x,1/4+y", "-z,-x,-y", "-z,1/2-x,1/2-y", "1/2-z,-x,1/2-y", "1/2-z,1/2-x,-y", "y,3/4-z,3/4-x", "y,1/4-z,1/4-x", "1/2+y,3/4-z,1/4-x", "1/2+y,1/4-z,3/4-x", "3/4-y,3/4-z,x", "3/4-y,1/4-z,1/2+x", "1/4-y,3/4-z,1/2+x", "1/4-y,1/4-z,x", "3/4-y,z,3/4-x", "3/4-y,1/2+z,1/4-x", "1/4-y,z,1/4-x", "1/4-y,1/2+z,3/4-x", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "1/4+x,-y,1/4+z", "1/4+x,1/2-y,3/4+z", "3/4+x,-y,3/4+z", "3/4+x,1/2-y,1/4+z", "-x,1/4+y,1/4+z", "-x,3/4+y,3/4+z", "1/2-x,1/4+y,3/4+z", "1/2-x,3/4+y,1/4+z", "1/4+x,1/4+y,-z", "1/4+x,3/4+y,1/2-z", "3/4+x,1/4+y,1/2-z", "3/4+x,3/4+y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "3/4-z,3/4-x,y", "3/4-z,1/4-x,1/2+y", "1/4-z,3/4-x,1/2+y", "1/4-z,1/4-x,y", "3/4-z,x,3/4-y", "3/4-z,1/2+x,1/4-y", "1/4-z,x,1/4-y", "1/4-z,1/2+x,3/4-y", "z,3/4-x,3/4-y", "z,1/4-x,1/4-y", "1/2+z,3/4-x,1/4-y", "1/2+z,1/4-x,3/4-y", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "-y,1/4+z,1/4+x", "-y,3/4+z,3/4+x", "1/2-y,1/4+z,3/4+x", "1/2-y,3/4+z,1/4+x", "1/4+y,1/4+z,-x", "1/4+y,3/4+z,1/2-x", "3/4+y,1/4+z,1/2-x", "3/4+y,3/4+z,-x", "1/4+y,-z,1/4+x", "1/4+y,1/2-z,3/4+x", "3/4+y,-z,3/4+x", "3/4+y,1/2-z,1/4+x", "-y,-z,-x", "-y,1/2-z,1/2-x", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x", "3/4-x,y,3/4-z", "3/4-x,1/2+y,1/4-z", "1/4-x,y,1/4-z", "1/4-x,1/2+y,3/4-z", "x,3/4-y,3/4-z", "x,1/4-y,1/4-z", "1/2+x,3/4-y,1/4-z", "1/2+x,1/4-y,3/4-z", "3/4-x,3/4-y,z", "3/4-x,1/4-y,1/2+z", "1/4-x,3/4-y,1/2+z", "1/4-x,1/4-y,z"]


hm_notation: P 42/m n m
symmetry_xyz:
["x,y,z", "-y,-x,z", "y,x,-z", "1/2+y,1/2-x,1/2-z", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "x,y,-z", "-x,-y,z", "y,x,z", "-y,-x,-z", "1/2-y,1/2+x,1/2-z", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: I -4 2 m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,-x,z", "1/2-y,1/2-x,1/2+z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "y,x,z", "1/2+y,1/2+x,1/2+z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: F d 3 m %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+z,3/4-x,1/4+y", "3/4+z,1/4-x,3/4+y", "1/4+z,3/4-x,3/4+y", "1/4+z,1/4-x,1/4+y", "-y,1/2+z,1/2-x", "-y,+z,-x", "1/2-y,1/2+z,-x", "1/2-y,+z,1/2-x", "3/4+x,3/4-y,1/4+z", "3/4+x,1/4-y,3/4+z", "1/4+x,3/4-y,3/4+z", "1/4+x,1/4-y,1/4+z", "-z,1/2+x,1/2-y", "-z,+x,-y", "1/2-z,1/2+x,-y", "1/2-z,+x,1/2-y", "3/4+y,3/4-z,1/4+x", "3/4+y,1/4-z,3/4+x", "1/4+y,3/4-z,3/4+x", "1/4+y,1/4-z,1/4+x", "-x,1/2+y,1/2-z", "-x,+y,-z", "1/2-x,1/2+y,-z", "1/2-x,+y,1/2-z", "1/2+x,-z,1/2-y", "1/2+x,1/2-z,-y", "+x,-z,-y", "+x,1/2-z,1/2-y", "3/4-z,3/4+y,1/4+x", "3/4-z,1/4+y,3/4+x", "1/4-z,3/4+y,3/4+x", "1/4-z,1/4+y,1/4+x", "1/2+y,-x,1/2-z", "1/2+y,1/2-x,-z", "+y,-x,-z", "+y,1/2-x,1/2-z", "3/4-x,3/4+z,1/4+y", "3/4-x,1/4+z,3/4+y", "1/4-x,3/4+z,3/4+y", "1/4-x,1/4+z,1/4+y", "1/2+z,-y,1/2-x", "1/2+z,1/2-y,-x", "+z,-y,-x", "+z,1/2-y,1/2-x", "3/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/4-y,3/4+x,3/4+z", "1/4-y,1/4+x,1/4+z", "x,1/2+z,1/2+y", "x,+z,+y", "1/2+x,1/2+z,+y", "1/2+x,+z,1/2+y", "1/4-z,3/4-y,3/4-x", "1/4-z,1/4-y,1/4-x", "3/4-z,3/4-y,1/4-x", "3/4-z,1/4-y,3/4-x", "y,1/2+x,1/2+z", "y,+x,+z", "1/2+y,1/2+x,+z", "1/2+y,+x,1/2+z", "1/4-x,3/4-z,3/4-y", "1/4-x,1/4-z,1/4-y", "3/4-x,3/4-z,1/4-y", "3/4-x,1/4-z,3/4-y", "z,1/2+y,1/2+x", "z,+y,+x", "1/2+z,1/2+y,+x", "1/2+z,+y,1/2+x", "1/4-y,3/4-x,3/4-z", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,1/4-z", "3/4-y,1/4-x,3/4-z", "3/4+z,1/4+x,3/4-y", "3/4+z,3/4+x,1/4-y", "1/4+z,1/4+x,1/4-y", "1/4+z,3/4+x,3/4-y", "-y,1/2-z,1/2+x", "-y,-z,+x", "1/2-y,1/2-z,+x", "1/2-y,-z,1/2+x", "3/4+x,1/4+y,3/4-z", "3/4+x,3/4+y,1/4-z", "1/4+x,1/4+y,1/4-z", "1/4+x,3/4+y,3/4-z", "-z,1/2-x,1/2+y", "-z,-x,+y", "1/2-z,1/2-x,+y", "1/2-z,-x,1/2+y", "3/4+y,1/4+z,3/4-x", "3/4+y,3/4+z,1/4-x", "1/4+y,1/4+z,1/4-x", "1/4+y,3/4+z,3/4-x", "-x,1/2-y,1/2+z", "-x,-y,+z", "1/2-x,1/2-y,+z", "1/2-x,-y,1/2+z", "1/4-z,3/4+x,3/4+y", "1/4-z,1/4+x,1/4+y", "3/4-z,3/4+x,1/4+y", "3/4-z,1/4+x,3/4+y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "1/4-x,3/4+y,3/4+z", "1/4-x,1/4+y,1/4+z", "3/4-x,3/4+y,1/4+z", "3/4-x,1/4+y,3/4+z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "1/4-y,3/4+z,3/4+x", "1/4-y,1/4+z,1/4+x", "3/4-y,3/4+z,1/4+x", "3/4-y,1/4+z,3/4+x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "1/2-x,1/2+z,-y", "1/2-x,+z,1/2-y", "-x,1/2+z,1/2-y", "-x,+z,-y", "1/4+z,3/4-y,3/4+x", "1/4+z,1/4-y,1/4+x", "3/4+z,3/4-y,1/4+x", "3/4+z,1/4-y,3/4+x", "1/2-y,1/2+x,-z", "1/2-y,+x,1/2-z", "-y,1/2+x,1/2-z", "-y,+x,-z", "1/4+x,3/4-z,3/4+y", "1/4+x,1/4-z,1/4+y", "3/4+x,3/4-z,1/4+y", "3/4+x,1/4-z,3/4+y", "1/2-z,1/2+y,-x", "1/2-z,+y,1/2-x", "-z,1/2+y,1/2-x", "-z,+y,-x", "1/4+y,3/4-x,3/4+z", "1/4+y,1/4-x,1/4+z", "3/4+y,3/4-x,1/4+z", "3/4+y,1/4-x,3/4+z", "-x,-z,y", "-x,1/2-z,1/2+y", "1/2-x,-z,1/2+y", "1/2-x,1/2-z,y", "3/4+z,3/4+y,1/4-x", "3/4+z,1/4+y,3/4-x", "1/4+z,3/4+y,3/4-x", "1/4+z,1/4+y,1/4-x", "-y,-x,z", "-y,1/2-x,1/2+z", "1/2-y,-x,1/2+z", "1/2-y,1/2-x,z", "3/4+x,3/4+z,1/4-y", "3/4+x,1/4+z,3/4-y", "1/4+x,3/4+z,3/4-y", "1/4+x,1/4+z,1/4-y", "-z,-y,x", "-z,1/2-y,1/2+x", "1/2-z,-y,1/2+x", "1/2-z,1/2-y,x", "3/4+y,3/4+x,1/4-z", "3/4+y,1/4+x,3/4-z", "1/4+y,3/4+x,3/4-z", "1/4+y,1/4+x,1/4-z", "1/4-z,1/4-x,1/4-y", "1/4-z,3/4-x,3/4-y", "3/4-z,1/4-x,3/4-y", "3/4-z,3/4-x,1/4-y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "1/4-x,1/4-y,1/4-z", "1/4-x,3/4-y,3/4-z", "3/4-x,1/4-y,3/4-z", "3/4-x,3/4-y,1/4-z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "1/4-y,1/4-z,1/4-x", "1/4-y,3/4-z,3/4-x", "3/4-y,1/4-z,3/4-x", "3/4-y,3/4-z,1/4-x"]


hm_notation: P 63 2 2
symmetry_xyz:
["x,y,z", "x,x-y,1/2-z", "x-y,x,1/2+z", "y,x,-z", "-y,x-y,z", "-x+y,y,1/2-z", "-x,-y,1/2+z", "-x,-x+y,-z", "-x+y,-x,z", "-y,-x,1/2-z", "y,-x+y,1/2+z", "x-y,-y,-z"]


hm_notation: P -6 2 c
symmetry_xyz:
["x,y,z", "-x,-x+y,1/2+z", "-x+y,-x,1/2-z", "y,x,-z", "-y,x-y,z", "x-y,-y,1/2+z", "x,y,1/2-z", "-x,-x+y,-z", "-x+y,-x,z", "y,x,1/2+z", "-y,x-y,1/2-z", "x-y,-y,-z"]


hm_notation: I -4 3 m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-z,x,-y", "1/2-z,1/2+x,1/2-y", "-y,z,-x", "1/2-y,1/2+z,1/2-x", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,-z,-y", "1/2+x,1/2-z,1/2-y", "z,-y,-x", "1/2+z,1/2-y,1/2-x", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "x,z,y", "1/2+x,1/2+z,1/2+y", "z,y,x", "1/2+z,1/2+y,1/2+x", "y,x,z", "1/2+y,1/2+x,1/2+z", "-z,-x,y", "1/2-z,1/2-x,1/2+y", "-y,-z,x", "1/2-y,1/2-z,1/2+x", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "z,-x,-y", "1/2+z,1/2-x,1/2-y", "y,-z,-x", "1/2+y,1/2-z,1/2-x", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,z,-y", "1/2-x,1/2+z,1/2-y", "-z,y,-x", "1/2-z,1/2+y,1/2-x", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "-x,-z,y", "1/2-x,1/2-z,1/2+y", "-z,-y,x", "1/2-z,1/2-y,1/2+x", "-y,-x,z", "1/2-y,1/2-x,1/2+z", "z,x,y", "1/2+z,1/2+x,1/2+y", "y,z,x", "1/2+y,1/2+z,1/2+x"]


hm_notation: R -3 m %var1%
symmetry_xyz:
["x,y,z", "-x,-z,-y", "-z,-x,-y", "y,x,z", "y,z,x", "-z,-y,-x", "-x,-y,-z", "x,z,y", "z,x,y", "-y,-x,-z", "-y,-z,-x", "z,y,x"]


hm_notation: P 4/m b m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "1/2+y,1/2+x,-z", "y,-x,-z", "-y,x,z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "x,y,-z", "-x,-y,z", "1/2+y,1/2+x,z", "1/2-y,1/2-x,-z", "-y,x,-z", "y,-x,z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "-x,-y,-z"]


hm_notation: P m n b
symmetry_xyz:
["x,y,z", "1/2-x,y,z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "-x,-y,-z"]


hm_notation: P b m n
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "x,-y,z", "-x,y,-z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "-x,-y,-z"]


hm_notation: C m m 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,z", "1/2-x,1/2+y,z", "-x,-y,z", "1/2-x,1/2-y,z"]


hm_notation: A m m 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,-y,z", "x,1/2-y,1/2+z", "-x,y,z", "-x,1/2+y,1/2+z", "-x,-y,z", "-x,1/2-y,1/2+z"]


hm_notation: C m m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "-x,y,z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2+x,1/2-y,-z", "x,y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2-x,1/2-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: B 1 21/d 1
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "3/4-x,1/2+y,3/4-z", "1/4-x,1/2+y,1/4-z", "3/4+x,1/2-y,3/4+z", "1/4+x,1/2-y,1/4+z", "1/2-x,-y,1/2-z", "-x,-y,-z"]


hm_notation: A b a 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,1/2-y,z", "1/2+x,-y,1/2+z", "1/2-x,1/2+y,z", "1/2-x,+y,1/2+z", "-x,-y,z", "-x,1/2-y,1/2+z"]


hm_notation: F -4 3 m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-z,-y", "x,1/2-z,1/2-y", "1/2+x,-z,1/2-y", "1/2+x,1/2-z,-y", "z,-y,-x", "z,1/2-y,1/2-x", "1/2+z,-y,1/2-x", "1/2+z,1/2-y,-x", "y,-x,-z", "y,1/2-x,1/2-z", "1/2+y,-x,1/2-z", "1/2+y,1/2-x,-z", "x,z,y", "x,1/2+z,1/2+y", "1/2+x,z,1/2+y", "1/2+x,1/2+z,y", "z,y,x", "z,1/2+y,1/2+x", "1/2+z,y,1/2+x", "1/2+z,1/2+y,x", "y,x,z", "y,1/2+x,1/2+z", "1/2+y,x,1/2+z", "1/2+y,1/2+x,z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,z,-y", "-x,1/2+z,1/2-y", "1/2-x,z,1/2-y", "1/2-x,1/2+z,-y", "-z,y,-x", "-z,1/2+y,1/2-x", "1/2-z,y,1/2-x", "1/2-z,1/2+y,-x", "-y,x,-z", "-y,1/2+x,1/2-z", "1/2-y,x,1/2-z", "1/2-y,1/2+x,-z", "-x,-z,y", "-x,1/2-z,1/2+y", "1/2-x,-z,1/2+y", "1/2-x,1/2-z,y", "-z,-y,x", "-z,1/2-y,1/2+x", "1/2-z,-y,1/2+x", "1/2-z,1/2-y,x", "-y,-x,z", "-y,1/2-x,1/2+z", "1/2-y,-x,1/2+z", "1/2-y,1/2-x,z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x"]


hm_notation: I a 3
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+z,x,1/2-y", "+z,1/2+x,-y", "1/2+z,-x,y", "+z,1/2-x,1/2+y", "-z,x,1/2+y", "1/2-z,1/2+x,+y", "-z,-x,-y", "1/2-z,1/2-x,1/2-y", "1/2+y,1/2-z,-x", "+y,-z,1/2-x", "-y,1/2-z,x", "1/2-y,-z,1/2+x", "1/2-y,z,-x", "-y,1/2+z,1/2-x", "y,z,x", "1/2+y,1/2+z,1/2+x", "x,1/2-y,1/2+z", "1/2+x,-y,+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z", "1/2-z,-x,1/2+y", "-z,1/2-x,+y", "1/2-z,x,-y", "-z,1/2+x,1/2-y", "z,-x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "1/2+z,1/2+x,1/2+y", "1/2-y,1/2+z,x", "-y,+z,1/2+x", "y,1/2+z,-x", "1/2+y,+z,1/2-x", "1/2+y,-z,x", "+y,1/2-z,1/2+x", "-y,-z,-x", "1/2-y,1/2-z,1/2-x", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,1/2-y,z", "1/2-x,-y,1/2+z"]


hm_notation: P m m n
symmetry_xyz:
["x,y,z", "x,1/2-y,z", "-x,1/2+y,-z", "1/2-x,y,z", "1/2+x,-y,-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-x,-y,-z"]


hm_notation: A 1 2/a 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,-y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P b a m
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "x,y,-z", "-x,-y,z", "-x,-y,-z"]


hm_notation: F -1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: P 4/n
symmetry_xyz:
["x,y,z", "1/2+y,-x,-z", "1/2-y,x,z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-y,1/2+x,-z", "y,1/2-x,z", "-x,-y,-z"]


hm_notation: P 62 2 2
symmetry_xyz:
["x,y,z", "x,x-y,1/3-z", "x-y,x,1/3+z", "y,x,2/3-z", "-y,x-y,2/3+z", "-x+y,y,-z", "-x,-y,z", "-x,-x+y,1/3-z", "-x+y,-x,1/3+z", "-y,-x,2/3-z", "y,-x+y,2/3+z", "x-y,-y,-z"]


hm_notation: R -3 c %var1%
symmetry_xyz:
["x,y,z", "1/2-x,1/2-z,1/2-y", "-z,-x,-y", "1/2+y,1/2+x,1/2+z", "y,z,x", "1/2-z,1/2-y,1/2-x", "-x,-y,-z", "1/2+x,1/2+z,1/2+y", "z,x,y", "1/2-y,1/2-x,1/2-z", "-y,-z,-x", "1/2+z,1/2+y,1/2+x"]


hm_notation: P 43 2 2
symmetry_xyz:
["x,y,z", "y,x,1/4-z", "-y,x,3/4+z", "-x,y,-z", "-x,-y,1/2+z", "-y,-x,3/4-z", "y,-x,1/4+z", "x,-y,1/2-z"]


hm_notation: I m m 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: R 3
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z"]


hm_notation: A b m 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,1/2-y,z", "x,-y,1/2+z", "-x,1/2+y,z", "-x,+y,1/2+z", "-x,-y,z", "-x,1/2-y,1/2+z"]


hm_notation: P 43 21 2
symmetry_xyz:
["x,y,z", "y,x,-z", "1/2-y,1/2+x,3/4+z", "1/2-x,1/2+y,3/4-z", "-x,-y,1/2+z", "-y,-x,1/2-z", "1/2+y,1/2-x,1/4+z", "1/2+x,1/2-y,1/4-z"]


hm_notation: A 1 2/m 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "x,-y,z", "x,1/2-y,1/2+z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: B m m b
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "-x,1/2-y,z", "1/2-x,1/2-y,1/2+z", "-x,y,z", "1/2-x,y,1/2+z", "x,-y,-z", "1/2+x,-y,1/2-z", "x,1/2-y,z", "1/2+x,1/2-y,1/2+z", "-x,1/2+y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: I 41/a m d %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,1/2-x,1/4+z", "1/2-y,-x,3/4+z", "1/2+y,1/2+x,1/2-z", "+y,+x,-z", "1/2+y,1/2-x,1/2-z", "+y,-x,-z", "-y,1/2+x,1/4+z", "1/2-y,+x,3/4+z", "1/2+x,1/2-y,1/2+z", "+x,-y,+z", "1/2-x,y,3/4-z", "-x,1/2+y,1/4-z", "1/2+x,y,3/4-z", "+x,1/2+y,1/4-z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z", "1/2+y,x,3/4+z", "+y,1/2+x,1/4+z", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "1/2+y,-x,3/4+z", "+y,1/2-x,1/4+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,1/2-y,1/4-z", "1/2+x,-y,3/4-z", "-x,1/2-y,1/4-z", "1/2-x,-y,3/4-z"]


hm_notation: P 6/m m m
symmetry_xyz:
["x,y,z", "-x,-x+y,z", "x,x-y,-z", "-x+y,-x,-z", "x-y,x,z", "-y,-x,z", "y,x,-z", "y,-x+y,-z", "-y,x-y,z", "x-y,-y,z", "-x+y,y,-z", "x,y,-z", "-x,-y,z", "x,x-y,z", "-x,-x+y,-z", "x-y,x,-z", "-x+y,-x,z", "y,x,z", "-y,-x,-z", "-y,x-y,-z", "y,-x+y,z", "-x+y,y,z", "x-y,-y,-z", "-x,-y,-z"]


hm_notation: P 4/n %var1%
symmetry_xyz:
["x,y,z", "y,-x,-z", "1/2-y,1/2+x,z", "1/2+x,1/2+y,-z", "-x,-y,z", "-y,x,-z", "1/2+y,1/2-x,z", "1/2-x,1/2-y,-z"]


hm_notation: B m a m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "1/2+x,y,-z", "+x,y,1/2-z", "1/2-x,-y,z", "-x,-y,1/2+z", "-x,y,z", "1/2-x,y,1/2+z", "x,-y,-z", "1/2+x,-y,1/2-z", "1/2+x,-y,z", "+x,-y,1/2+z", "1/2-x,y,-z", "-x,y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: F d d 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,1/4-y,1/4+z", "1/4+x,3/4-y,3/4+z", "3/4+x,1/4-y,3/4+z", "3/4+x,3/4-y,1/4+z", "1/4-x,1/4+y,1/4+z", "1/4-x,3/4+y,3/4+z", "3/4-x,1/4+y,3/4+z", "3/4-x,3/4+y,1/4+z", "-x,1/2-y,1/2+z", "-x,-y,+z", "1/2-x,1/2-y,+z", "1/2-x,-y,1/2+z"]


hm_notation: I b a m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 2 2 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: P c a b
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "-x,-y,-z"]


hm_notation: P m 3 n
symmetry_xyz:
["x,y,z", "z,-x,y", "-y,z,-x", "x,-y,z", "-z,x,-y", "y,-z,x", "-x,y,-z", "1/2+x,1/2-z,1/2-y", "1/2-z,1/2+y,1/2+x", "1/2+y,1/2-x,1/2-z", "1/2-x,1/2+z,1/2+y", "1/2+z,1/2-y,1/2-x", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2+z,1/2+y", "1/2-z,1/2-y,1/2-x", "1/2+y,1/2+x,1/2+z", "1/2-x,1/2-z,1/2-y", "1/2+z,1/2+y,1/2+x", "1/2-y,1/2-x,1/2-z", "z,x,-y", "-y,-z,x", "x,y,-z", "-z,-x,y", "y,z,-x", "-x,-y,z", "-z,x,y", "y,-z,-x", "-x,y,z", "z,-x,-y", "-y,z,x", "x,-y,-z", "1/2-x,1/2+z,1/2-y", "1/2+z,1/2-y,1/2+x", "1/2-y,1/2+x,1/2-z", "1/2+x,1/2-z,1/2+y", "1/2-z,1/2+y,1/2-x", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2-z,1/2+y", "1/2+z,1/2+y,1/2-x", "1/2-y,1/2-x,1/2+z", "1/2+x,1/2+z,1/2-y", "1/2-z,1/2-y,1/2+x", "1/2+y,1/2+x,1/2-z", "-z,-x,-y", "y,z,x", "-x,-y,-z", "z,x,y", "-y,-z,-x"]


hm_notation: I m m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: C 1 1 21/d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/4+x,1/4+y,1/2-z", "3/4+x,3/4+y,1/2-z", "1/4-x,1/4-y,1/2+z", "3/4-x,3/4-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: P 4/n c c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,1/2-z", "1/2+y,-x,-z", "1/2-y,x,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,1/2+x,-z", "y,1/2-x,z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "-x,-y,-z"]


hm_notation: P 42/m b c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,1/2-z", "y,-x,1/2-z", "-y,x,1/2+z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "x,y,-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "1/2-y,1/2-x,1/2-z", "-y,x,1/2-z", "y,-x,1/2+z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "-x,-y,-z"]


hm_notation: I m 3 m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "z,-x,y", "1/2+z,1/2-x,1/2+y", "-y,z,-x", "1/2-y,1/2+z,1/2-x", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-z,x,-y", "1/2-z,1/2+x,1/2-y", "y,-z,x", "1/2+y,1/2-z,1/2+x", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,-z,-y", "1/2+x,1/2-z,1/2-y", "-z,y,x", "1/2-z,1/2+y,1/2+x", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-x,z,y", "1/2-x,1/2+z,1/2+y", "z,-y,-x", "1/2+z,1/2-y,1/2-x", "-y,x,z", "1/2-y,1/2+x,1/2+z", "x,z,y", "1/2+x,1/2+z,1/2+y", "-z,-y,-x", "1/2-z,1/2-y,1/2-x", "y,x,z", "1/2+y,1/2+x,1/2+z", "-x,-z,-y", "1/2-x,1/2-z,1/2-y", "z,y,x", "1/2+z,1/2+y,1/2+x", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "z,x,-y", "1/2+z,1/2+x,1/2-y", "-y,-z,x", "1/2-y,1/2-z,1/2+x", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-z,-x,y", "1/2-z,1/2-x,1/2+y", "y,z,-x", "1/2+y,1/2+z,1/2-x", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-z,x,y", "1/2-z,1/2+x,1/2+y", "y,-z,-x", "1/2+y,1/2-z,1/2-x", "-x,y,z", "1/2-x,1/2+y,1/2+z", "z,-x,-y", "1/2+z,1/2-x,1/2-y", "-y,z,x", "1/2-y,1/2+z,1/2+x", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,z,-y", "1/2-x,1/2+z,1/2-y", "z,-y,x", "1/2+z,1/2-y,1/2+x", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "x,-z,y", "1/2+x,1/2-z,1/2+y", "-z,y,-x", "1/2-z,1/2+y,1/2-x", "y,-x,z", "1/2+y,1/2-x,1/2+z", "-x,-z,y", "1/2-x,1/2-z,1/2+y", "z,y,-x", "1/2+z,1/2+y,1/2-x", "-y,-x,z", "1/2-y,1/2-x,1/2+z", "x,z,-y", "1/2+x,1/2+z,1/2-y", "-z,-y,x", "1/2-z,1/2-y,1/2+x", "y,x,-z", "1/2+y,1/2+x,1/2-z", "-z,-x,-y", "1/2-z,1/2-x,1/2-y", "y,z,x", "1/2+y,1/2+z,1/2+x", "-x,-y,-z", "1/2-x,1/2-y,1/2-z", "z,x,y", "1/2+z,1/2+x,1/2+y", "-y,-z,-x", "1/2-y,1/2-z,1/2-x"]


hm_notation: P 42/n n m
symmetry_xyz:
["x,y,z", "-y,-x,z", "1/2+y,1/2+x,1/2-z", "y,-x,-z", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "y,x,z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: B m a b
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "x,1/2+y,1/2-z", "1/2+x,1/2+y,-z", "-x,1/2-y,1/2+z", "1/2-x,1/2-y,+z", "-x,y,z", "1/2-x,y,1/2+z", "x,-y,-z", "1/2+x,-y,1/2-z", "x,1/2-y,1/2+z", "1/2+x,1/2-y,+z", "-x,1/2+y,1/2-z", "1/2-x,1/2+y,-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P 4 21 2
symmetry_xyz:
["x,y,z", "y,x,-z", "1/2-y,1/2+x,z", "1/2-x,1/2+y,-z", "-x,-y,z", "-y,-x,-z", "1/2+y,1/2-x,z", "1/2+x,1/2-y,-z"]


hm_notation: F d d d %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+x,1/4-y,3/4+z", "3/4+x,3/4-y,1/4+z", "1/4+x,1/4-y,1/4+z", "1/4+x,3/4-y,3/4+z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "1/4-x,3/4+y,3/4+z", "1/4-x,1/4+y,1/4+z", "3/4-x,3/4+y,1/4+z", "3/4-x,1/4+y,3/4+z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "3/4+x,3/4+y,1/4-z", "3/4+x,1/4+y,3/4-z", "1/4+x,3/4+y,3/4-z", "1/4+x,1/4+y,1/4-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "1/4-x,1/4-y,1/4-z", "1/4-x,3/4-y,3/4-z", "3/4-x,1/4-y,3/4-z", "3/4-x,3/4-y,1/4-z"]


hm_notation: P 43 3 2
symmetry_xyz:
["x,y,z", "-z,1/2+x,1/2-y", "-y,1/2+z,1/2-x", "-x,1/2+y,1/2-z", "3/4-x,1/4+z,3/4+y", "3/4-z,1/4+y,3/4+x", "3/4-y,1/4+x,3/4+z", "1/4-x,1/4-z,1/4-y", "1/4-z,1/4-y,1/4-x", "1/4-y,1/4-x,1/4-z", "1/2-z,-x,1/2+y", "1/2-y,-z,1/2+x", "1/2-x,-y,1/2+z", "1/2+z,1/2-x,-y", "1/2+y,1/2-z,-x", "1/2+x,1/2-y,-z", "3/4+x,3/4-z,1/4+y", "3/4+z,3/4-y,1/4+x", "3/4+y,3/4-x,1/4+z", "1/4+x,3/4+z,3/4-y", "1/4+z,3/4+y,3/4-x", "1/4+y,3/4+x,3/4-z", "z,x,y", "y,z,x"]


hm_notation: P b m a
symmetry_xyz:
["x,y,z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "1/2+x,y,-z", "1/2-x,-y,z", "x,1/2-y,z", "-x,1/2+y,-z", "-x,-y,-z"]


hm_notation: I 41 2 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+y,1/2+x,1/2-z", "+y,+x,-z", "-y,1/2+x,1/4+z", "1/2-y,+x,3/4+z", "1/2-x,y,3/4-z", "-x,1/2+y,1/4-z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "1/2+y,-x,3/4+z", "+y,1/2-x,1/4+z", "x,1/2-y,1/4-z", "1/2+x,-y,3/4-z"]


hm_notation: P 42/n c m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "1/2+y,1/2+x,-z", "1/2+y,-x,1/2-z", "1/2-y,x,1/2+z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "y,x,z", "-y,-x,-z", "-y,1/2+x,1/2-z", "y,1/2-x,1/2+z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "-x,-y,-z"]


hm_notation: P 42/n
symmetry_xyz:
["x,y,z", "y,1/2-x,1/2-z", "-y,1/2+x,1/2+z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "1/2-y,x,1/2-z", "1/2+y,-x,1/2+z", "-x,-y,-z"]


hm_notation: P 42/n m c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "y,x,-z", "y,-x,-z", "1/2-y,1/2+x,1/2+z", "x,-y,z", "1/2-x,1/2+y,1/2-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "-y,-x,-z", "-y,x,-z", "1/2+y,1/2-x,1/2+z", "-x,y,z", "1/2+x,1/2-y,1/2-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 41/a %var2%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+y,1/2-x,1/2-z", "+y,-x,-z", "-y,1/2+x,1/4+z", "1/2-y,+x,3/4+z", "1/2+x,y,3/4-z", "+x,1/2+y,1/4-z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "1/2+y,-x,3/4+z", "+y,1/2-x,1/4+z", "-x,1/2-y,1/4-z", "1/2-x,-y,3/4-z"]


hm_notation: B b m m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "-x,1/2+y,z", "1/2-x,1/2+y,1/2+z", "x,1/2-y,-z", "1/2+x,1/2-y,1/2-z", "x,y,-z", "1/2+x,y,1/2-z", "-x,-y,z", "1/2-x,-y,1/2+z", "x,1/2-y,z", "1/2+x,1/2-y,1/2+z", "-x,1/2+y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P m m n %var1%
symmetry_xyz:
["x,y,z", "x,-y,z", "1/2-x,1/2+y,-z", "-x,y,z", "1/2+x,1/2-y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2-x,1/2-y,-z"]


hm_notation: C c m b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,1/2+z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "+x,-y,1/2-z", "x,1/2-y,z", "1/2+x,-y,z", "1/2-x,y,-z", "-x,1/2+y,-z", "1/2+x,y,1/2-z", "+x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,-z", "-x,-y,-z"]


hm_notation: P n m m
symmetry_xyz:
["x,y,z", "x,y,1/2-z", "-x,-y,1/2+z", "x,1/2-y,z", "-x,1/2+y,-z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: P n a a
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2-z", "1/2-x,-y,1/2+z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: F m m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: P n 3
symmetry_xyz:
["x,y,z", "1/2+z,1/2+x,-y", "1/2+z,-x,1/2+y", "-z,1/2+x,1/2+y", "-z,-x,-y", "y,1/2-z,1/2-x", "1/2-y,1/2-z,x", "1/2-y,z,1/2-x", "y,z,x", "1/2+x,-y,1/2+z", "-x,1/2+y,1/2+z", "1/2+x,1/2+y,-z", "-x,-y,-z", "1/2-z,1/2-x,y", "1/2-z,x,1/2-y", "z,1/2-x,1/2-y", "z,x,y", "-y,1/2+z,1/2+x", "1/2+y,1/2+z,-x", "1/2+y,-z,1/2+x", "-y,-z,-x", "1/2-x,y,1/2-z", "x,1/2-y,1/2-z", "1/2-x,1/2-y,z"]


hm_notation: I 2 3
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-z,-x,y", "1/2-z,1/2-x,1/2+y", "-z,x,-y", "1/2-z,1/2+x,1/2-y", "z,-x,-y", "1/2+z,1/2-x,1/2-y", "z,x,y", "1/2+z,1/2+x,1/2+y", "y,-z,-x", "1/2+y,1/2-z,1/2-x", "-y,-z,x", "1/2-y,1/2-z,1/2+x", "-y,z,-x", "1/2-y,1/2+z,1/2-x", "y,z,x", "1/2+y,1/2+z,1/2+x", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: P c a n
symmetry_xyz:
["x,y,z", "-x,y,1/2+z", "x,-y,1/2-z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z"]


hm_notation: P 4/n c c %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "y,x,1/2-z", "y,-x,-z", "1/2-y,1/2+x,z", "x,-y,1/2+z", "1/2-x,1/2+y,1/2-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "-y,-x,1/2-z", "-y,x,-z", "1/2+y,1/2-x,z", "-x,y,1/2+z", "1/2+x,1/2-y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: P 41 3 2
symmetry_xyz:
["x,y,z", "-z,1/2+x,1/2-y", "-y,1/2+z,1/2-x", "-x,1/2+y,1/2-z", "1/4-x,3/4+z,1/4+y", "1/4-z,3/4+y,1/4+x", "1/4-y,3/4+x,1/4+z", "3/4-x,3/4-z,3/4-y", "3/4-z,3/4-y,3/4-x", "3/4-y,3/4-x,3/4-z", "1/2-z,-x,1/2+y", "1/2-y,-z,1/2+x", "1/2-x,-y,1/2+z", "1/2+z,1/2-x,-y", "1/2+y,1/2-z,-x", "1/2+x,1/2-y,-z", "1/4+x,1/4-z,3/4+y", "1/4+z,1/4-y,3/4+x", "1/4+y,1/4-x,3/4+z", "3/4+x,1/4+z,1/4-y", "3/4+z,1/4+y,1/4-x", "3/4+y,1/4+x,1/4-z", "z,x,y", "y,z,x"]


hm_notation: A c m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,-y,1/2+z", "x,1/2-y,+z", "-x,y,1/2-z", "-x,1/2+y,-z", "x,y,-z", "x,1/2+y,1/2-z", "-x,-y,z", "-x,1/2-y,1/2+z", "-x,y,1/2+z", "-x,1/2+y,+z", "x,-y,1/2-z", "x,1/2-y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P 42/m c m
symmetry_xyz:
["x,y,z", "-y,-x,z", "y,x,-z", "y,-x,1/2-z", "-y,x,1/2+z", "x,-y,1/2+z", "-x,y,1/2-z", "x,y,-z", "-x,-y,z", "y,x,z", "-y,-x,-z", "-y,x,1/2-z", "y,-x,1/2+z", "-x,y,1/2+z", "x,-y,1/2-z", "-x,-y,-z"]


hm_notation: F d 2 d
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4-x,1/4+y,1/4+z", "1/4-x,3/4+y,3/4+z", "3/4-x,1/4+y,3/4+z", "3/4-x,3/4+y,1/4+z", "1/4+x,1/4+y,1/4-z", "1/4+x,3/4+y,3/4-z", "3/4+x,1/4+y,3/4-z", "3/4+x,3/4+y,1/4-z", "1/2-x,1/2+y,-z", "1/2-x,+y,1/2-z", "-x,1/2+y,1/2-z", "-x,+y,-z"]


hm_notation: B 1 1 2/b
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "-x,1/2-y,z", "1/2-x,1/2-y,1/2+z", "x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P 4/m c c
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "y,x,1/2-z", "y,-x,-z", "-y,x,z", "x,-y,1/2+z", "-x,y,1/2-z", "x,y,-z", "-x,-y,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,x,-z", "y,-x,z", "-x,y,1/2+z", "x,-y,1/2-z", "-x,-y,-z"]


hm_notation: P 2 3
symmetry_xyz:
["x,y,z", "-z,-x,y", "-z,x,-y", "z,-x,-y", "z,x,y", "y,-z,-x", "-y,-z,x", "-y,z,-x", "y,z,x", "-x,y,-z", "x,-y,-z", "-x,-y,z"]


hm_notation: A m a 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,-y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,y,z", "1/2-x,1/2+y,1/2+z", "-x,-y,z", "-x,1/2-y,1/2+z"]


hm_notation: P 42/m m c
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "y,x,1/2-z", "y,-x,1/2-z", "-y,x,1/2+z", "x,-y,z", "-x,y,-z", "x,y,-z", "-x,-y,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,x,1/2-z", "y,-x,1/2+z", "-x,y,z", "x,-y,-z", "-x,-y,-z"]


hm_notation: P 42/n m c %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,-z", "1/2+y,-x,-z", "1/2-y,x,1/2+z", "x,1/2-y,z", "-x,1/2+y,1/2-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,z", "y,x,1/2+z", "-y,-x,-z", "-y,1/2+x,-z", "y,1/2-x,1/2+z", "1/2-x,y,z", "1/2+x,-y,1/2-z", "-x,-y,1/2-z"]


hm_notation: I m a 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+x,1/2-y,z", "+x,-y,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "1/2-x,1/2-y,z", "-x,-y,1/2+z"]


hm_notation: F d 3 %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+z,1/4+x,1/4-y", "1/4+z,3/4+x,3/4-y", "3/4+z,1/4+x,3/4-y", "3/4+z,3/4+x,1/4-y", "1/4+z,1/4-x,1/4+y", "1/4+z,3/4-x,3/4+y", "3/4+z,1/4-x,3/4+y", "3/4+z,3/4-x,1/4+y", "1/4-z,1/4+x,1/4+y", "1/4-z,3/4+x,3/4+y", "3/4-z,1/4+x,3/4+y", "3/4-z,3/4+x,1/4+y", "1/4-z,1/4-x,1/4-y", "1/4-z,3/4-x,3/4-y", "3/4-z,1/4-x,3/4-y", "3/4-z,3/4-x,1/4-y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "1/4+x,1/4-y,1/4+z", "1/4+x,3/4-y,3/4+z", "3/4+x,1/4-y,3/4+z", "3/4+x,3/4-y,1/4+z", "1/4-x,1/4+y,1/4+z", "1/4-x,3/4+y,3/4+z", "3/4-x,1/4+y,3/4+z", "3/4-x,3/4+y,1/4+z", "1/4+x,1/4+y,1/4-z", "1/4+x,3/4+y,3/4-z", "3/4+x,1/4+y,3/4-z", "3/4+x,3/4+y,1/4-z", "1/4-x,1/4-y,1/4-z", "1/4-x,3/4-y,3/4-z", "3/4-x,1/4-y,3/4-z", "3/4-x,3/4-y,1/4-z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "1/4-y,1/4+z,1/4+x", "1/4-y,3/4+z,3/4+x", "3/4-y,1/4+z,3/4+x", "3/4-y,3/4+z,1/4+x", "1/4+y,1/4+z,1/4-x", "1/4+y,3/4+z,3/4-x", "3/4+y,1/4+z,3/4-x", "3/4+y,3/4+z,1/4-x", "1/4+y,1/4-z,1/4+x", "1/4+y,3/4-z,3/4+x", "3/4+y,1/4-z,3/4+x", "3/4+y,3/4-z,1/4+x", "1/4-y,1/4-z,1/4-x", "1/4-y,3/4-z,3/4-x", "3/4-y,1/4-z,3/4-x", "3/4-y,3/4-z,1/4-x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z"]


hm_notation: I 1 1 2/a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-x,-y,z", "-x,1/2-y,1/2+z", "1/2+x,y,-z", "+x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: F 41 3 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-z,1/2+x,1/2-y", "-z,+x,-y", "1/2-z,1/2+x,-y", "1/2-z,+x,1/2-y", "-y,1/2+z,1/2-x", "-y,+z,-x", "1/2-y,1/2+z,-x", "1/2-y,+z,1/2-x", "-x,1/2+y,1/2-z", "-x,+y,-z", "1/2-x,1/2+y,-z", "1/2-x,+y,1/2-z", "3/4-x,3/4+z,1/4+y", "3/4-x,1/4+z,3/4+y", "1/4-x,3/4+z,3/4+y", "1/4-x,1/4+z,1/4+y", "3/4-z,3/4+y,1/4+x", "3/4-z,1/4+y,3/4+x", "1/4-z,3/4+y,3/4+x", "1/4-z,1/4+y,1/4+x", "3/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/4-y,3/4+x,3/4+z", "1/4-y,1/4+x,1/4+z", "1/4-x,3/4-z,3/4-y", "1/4-x,1/4-z,1/4-y", "3/4-x,3/4-z,1/4-y", "3/4-x,1/4-z,3/4-y", "1/4-z,3/4-y,3/4-x", "1/4-z,1/4-y,1/4-x", "3/4-z,3/4-y,1/4-x", "3/4-z,1/4-y,3/4-x", "1/4-y,3/4-x,3/4-z", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,1/4-z", "3/4-y,1/4-x,3/4-z", "-z,1/2-x,1/2+y", "-z,-x,+y", "1/2-z,1/2-x,+y", "1/2-z,-x,1/2+y", "-y,1/2-z,1/2+x", "-y,-z,+x", "1/2-y,1/2-z,+x", "1/2-y,-z,1/2+x", "-x,1/2-y,1/2+z", "-x,-y,+z", "1/2-x,1/2-y,+z", "1/2-x,-y,1/2+z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "1/4+x,3/4-z,3/4+y", "1/4+x,1/4-z,1/4+y", "3/4+x,3/4-z,1/4+y", "3/4+x,1/4-z,3/4+y", "1/4+z,3/4-y,3/4+x", "1/4+z,1/4-y,1/4+x", "3/4+z,3/4-y,1/4+x", "3/4+z,1/4-y,3/4+x", "1/4+y,3/4-x,3/4+z", "1/4+y,1/4-x,1/4+z", "3/4+y,3/4-x,1/4+z", "3/4+y,1/4-x,3/4+z", "3/4+x,3/4+z,1/4-y", "3/4+x,1/4+z,3/4-y", "1/4+x,3/4+z,3/4-y", "1/4+x,1/4+z,1/4-y", "3/4+z,3/4+y,1/4-x", "3/4+z,1/4+y,3/4-x", "1/4+z,3/4+y,3/4-x", "1/4+z,1/4+y,1/4-x", "3/4+y,3/4+x,1/4-z", "3/4+y,1/4+x,3/4-z", "1/4+y,3/4+x,3/4-z", "1/4+y,1/4+x,1/4-z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x"]


hm_notation: I 4 2 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "y,x,-z", "1/2+y,1/2+x,1/2-z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "y,-x,z", "1/2+y,1/2-x,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: I 4 3 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-z,x,-y", "1/2-z,1/2+x,1/2-y", "-y,z,-x", "1/2-y,1/2+z,1/2-x", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,z,y", "1/2-x,1/2+z,1/2+y", "-z,y,x", "1/2-z,1/2+y,1/2+x", "-y,x,z", "1/2-y,1/2+x,1/2+z", "-x,-z,-y", "1/2-x,1/2-z,1/2-y", "-z,-y,-x", "1/2-z,1/2-y,1/2-x", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "-z,-x,y", "1/2-z,1/2-x,1/2+y", "-y,-z,x", "1/2-y,1/2-z,1/2+x", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "z,-x,-y", "1/2+z,1/2-x,1/2-y", "y,-z,-x", "1/2+y,1/2-z,1/2-x", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "x,-z,y", "1/2+x,1/2-z,1/2+y", "z,-y,x", "1/2+z,1/2-y,1/2+x", "y,-x,z", "1/2+y,1/2-x,1/2+z", "x,z,-y", "1/2+x,1/2+z,1/2-y", "z,y,-x", "1/2+z,1/2+y,1/2-x", "y,x,-z", "1/2+y,1/2+x,1/2-z", "z,x,y", "1/2+z,1/2+x,1/2+y", "y,z,x", "1/2+y,1/2+z,1/2+x"]


hm_notation: P c n n
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-x,y,1/2+z", "x,-y,1/2-z", "-x,-y,-z"]


hm_notation: I -4 c 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "y,x,1/2-z", "1/2+y,1/2+x,-z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-y,-x,1/2-z", "1/2-y,1/2-x,-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "-x,y,1/2+z", "1/2-x,1/2+y,+z"]


hm_notation: C 2 2 21
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,1/2-z", "1/2-x,1/2+y,1/2-z", "x,-y,-z", "1/2+x,1/2-y,-z", "-x,-y,1/2+z", "1/2-x,1/2-y,1/2+z"]


hm_notation: P n a n
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "1/2+x,-y,z", "1/2-x,y,-z", "-x,-y,-z"]


hm_notation: P 41 2 2
symmetry_xyz:
["x,y,z", "y,x,3/4-z", "-y,x,1/4+z", "-x,y,-z", "-x,-y,1/2+z", "-y,-x,1/4-z", "y,-x,3/4+z", "x,-y,1/2-z"]


hm_notation: P 42 n m
symmetry_xyz:
["x,y,z", "-y,-x,z", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,-y,z", "y,x,z", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2+y,1/2+z"]


hm_notation: I -4 m 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "y,x,-z", "1/2+y,1/2+x,1/2-z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "-x,y,z", "1/2-x,1/2+y,1/2+z"]


hm_notation: C c c a %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,1/2-z", "-x,1/2+y,1/2+z", "1/2-x,+y,1/2+z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "x,1/2+y,-z", "1/2+x,+y,-z", "-x,1/2-y,z", "1/2-x,-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: I b c a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2-y,1/2+z", "1/2+x,-y,+z", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "-x,1/2-y,z", "1/2-x,-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P b n a
symmetry_xyz:
["x,y,z", "-x,1/2+y,z", "x,1/2-y,-z", "1/2+x,y,1/2-z", "1/2-x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z"]


hm_notation: P m n a
symmetry_xyz:
["x,y,z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,y,z", "x,-y,-z", "1/2+x,y,1/2-z", "1/2-x,-y,1/2+z", "-x,-y,-z"]


hm_notation: I 4 m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,-x,z", "1/2-y,1/2-x,1/2+z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "y,x,z", "1/2+y,1/2+x,1/2+z", "y,-x,z", "1/2+y,1/2-x,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z"]


hm_notation: I 41/a c d %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/4-y,3/4-x,3/4+z", "3/4-y,1/4-x,1/4+z", "1/4+y,3/4+x,3/4-z", "3/4+y,1/4+x,1/4-z", "1/4+y,3/4-x,1/4-z", "3/4+y,1/4-x,3/4-z", "1/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "+x,1/2+y,-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "1/4+y,1/4+x,1/4+z", "3/4+y,3/4+x,3/4+z", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,3/4-z", "1/4-y,1/4+x,3/4-z", "3/4-y,3/4+x,1/4-z", "1/4+y,1/4-x,3/4+z", "3/4+y,3/4-x,1/4+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I m 3
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "z,x,-y", "1/2+z,1/2+x,1/2-y", "z,-x,y", "1/2+z,1/2-x,1/2+y", "-z,x,y", "1/2-z,1/2+x,1/2+y", "-z,-x,-y", "1/2-z,1/2-x,1/2-y", "y,-z,-x", "1/2+y,1/2-z,1/2-x", "-y,-z,x", "1/2-y,1/2-z,1/2+x", "-y,z,-x", "1/2-y,1/2+z,1/2-x", "y,z,x", "1/2+y,1/2+z,1/2+x", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z", "-z,-x,y", "1/2-z,1/2-x,1/2+y", "-z,x,-y", "1/2-z,1/2+x,1/2-y", "z,-x,-y", "1/2+z,1/2-x,1/2-y", "z,x,y", "1/2+z,1/2+x,1/2+y", "-y,z,x", "1/2-y,1/2+z,1/2+x", "y,z,-x", "1/2+y,1/2+z,1/2-x", "y,-z,x", "1/2+y,1/2-z,1/2+x", "-y,-z,-x", "1/2-y,1/2-z,1/2-x", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: P m a b
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "x,1/2+y,-z", "-x,1/2-y,z", "1/2-x,y,z", "1/2+x,-y,-z", "-x,-y,-z"]


hm_notation: P 42/n n m %var1%
symmetry_xyz:
["x,y,z", "-y,-x,z", "y,x,-z", "1/2+y,-x,1/2-z", "1/2-y,x,1/2+z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "1/2+y,1/2+x,z", "1/2-y,1/2-x,-z", "-y,1/2+x,1/2-z", "y,1/2-x,1/2+z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: P m c b
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "-x,y,z", "x,-y,-z", "-x,-y,-z"]


hm_notation: P 4/m n c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,1/2-z", "y,-x,-z", "-y,x,z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "x,y,-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "y,-x,z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: F m m 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z"]


hm_notation: I m m a %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "1/2+x,-y,-z", "x,1/2+y,1/2-z", "1/2+x,+y,-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-x,1/2-y,1/2-z", "1/2-x,-y,-z"]


hm_notation: I 21 21 21
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "1/2+x,-y,-z", "+x,1/2-y,1/2-z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z"]


hm_notation: I 2 m b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2+y,1/2-z", "1/2+x,+y,-z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "x,1/2-y,1/2-z", "1/2+x,-y,-z"]


hm_notation: C m m a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/2+x,-y,z", "+x,1/2-y,z", "1/2-x,y,-z", "-x,1/2+y,-z", "-x,y,z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2+x,1/2-y,-z", "1/2+x,y,-z", "+x,1/2+y,-z", "1/2-x,-y,z", "-x,1/2-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: I 21 3
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-z,-x,1/2+y", "-z,1/2-x,+y", "-z,1/2+x,1/2-y", "1/2-z,+x,-y", "1/2+z,1/2-x,-y", "+z,-x,1/2-y", "z,x,y", "1/2+z,1/2+x,1/2+y", "1/2+y,1/2-z,-x", "+y,-z,1/2-x", "1/2-y,-z,1/2+x", "-y,1/2-z,+x", "-y,1/2+z,1/2-x", "1/2-y,+z,-x", "y,z,x", "1/2+y,1/2+z,1/2+x", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "1/2+x,1/2-y,-z", "+x,-y,1/2-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z"]


hm_notation: P -4 n 2
symmetry_xyz:
["x,y,z", "1/2+y,1/2+x,1/2-z", "y,-x,-z", "1/2+x,1/2-y,1/2+z", "-x,-y,z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "1/2-x,1/2+y,1/2+z"]


hm_notation: B m 2 m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "-x,y,z", "1/2-x,y,1/2+z", "x,y,-z", "1/2+x,y,1/2-z", "-x,y,-z", "1/2-x,y,1/2-z"]


hm_notation: A m m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,y,-z", "x,1/2+y,1/2-z", "-x,-y,z", "-x,1/2-y,1/2+z", "x,-y,z", "x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "-x,y,z", "-x,1/2+y,1/2+z", "x,-y,-z", "x,1/2-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: C m 2 a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/2-x,y,z", "-x,1/2+y,z", "1/2+x,y,-z", "+x,1/2+y,-z", "-x,y,-z", "1/2-x,1/2+y,-z"]


hm_notation: A 2 m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,y,-z", "x,1/2+y,1/2-z", "x,-y,z", "x,1/2-y,1/2+z", "x,-y,-z", "x,1/2-y,1/2-z"]


hm_notation: A b m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,1/2+y,-z", "x,+y,1/2-z", "-x,1/2-y,z", "-x,-y,1/2+z", "x,-y,z", "x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "-x,1/2+y,z", "-x,+y,1/2+z", "x,1/2-y,-z", "x,-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: I m 2 m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,y,-z", "1/2-x,1/2+y,1/2-z"]


hm_notation: F 2 3
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z"]


hm_notation: P b a n
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2-x,1/2-y,-z"]


hm_notation: P -4 b 2
symmetry_xyz:
["x,y,z", "1/2+y,1/2+x,-z", "y,-x,-z", "1/2+x,1/2-y,z", "-x,-y,z", "1/2-y,1/2-x,-z", "-y,x,-z", "1/2-x,1/2+y,z"]


hm_notation: C c m 21
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,1/2+z", "1/2-x,1/2+y,1/2+z", "x,-y,z", "1/2+x,1/2-y,z", "-x,-y,1/2+z", "1/2-x,1/2-y,1/2+z"]


hm_notation: I m a m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,y,1/2-z", "1/2+x,1/2+y,-z", "-x,-y,1/2+z", "1/2-x,1/2-y,+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P m 3
symmetry_xyz:
["x,y,z", "z,x,-y", "z,-x,y", "-z,x,y", "-z,-x,-y", "y,-z,-x", "-y,-z,x", "-y,z,-x", "y,z,x", "x,-y,z", "-x,y,z", "x,y,-z", "-x,-y,-z", "-z,-x,y", "-z,x,-y", "z,-x,-y", "z,x,y", "-y,z,x", "y,z,-x", "y,-z,x", "-y,-z,-x", "-x,y,-z", "x,-y,-z", "-x,-y,z"]


hm_notation: I 1 1 2/b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,1/2-y,z", "1/2-x,-y,1/2+z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P n 3 %var1%
symmetry_xyz:
["x,y,z", "1/2+z,1/2+x,1/2-y", "1/2+z,1/2-x,1/2+y", "1/2-z,1/2+x,1/2+y", "1/2-z,1/2-x,1/2-y", "y,-z,-x", "-y,-z,x", "-y,z,-x", "y,z,x", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2-z", "-z,-x,y", "-z,x,-y", "z,-x,-y", "z,x,y", "1/2-y,1/2+z,1/2+x", "1/2+y,1/2+z,1/2-x", "1/2+y,1/2-z,1/2+x", "1/2-y,1/2-z,1/2-x", "-x,y,-z", "x,-y,-z", "-x,-y,z"]


hm_notation: P n c b
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2-z", "-x,-y,z", "x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2+z", "x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: A m m a
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,-y,z", "1/2-x,1/2-y,1/2+z", "x,-y,z", "x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,z", "1/2-x,1/2+y,1/2+z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: I 2 c m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "x,y,1/2-z", "1/2+x,1/2+y,-z", "x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: I 4
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "y,-x,z", "1/2+y,1/2-x,1/2+z"]


hm_notation: I 41 3 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-z,1/2+x,1/2-y", "1/2-z,+x,-y", "-y,1/2+z,1/2-x", "1/2-y,+z,-x", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "3/4-x,1/4+z,3/4+y", "1/4-x,3/4+z,1/4+y", "3/4-z,1/4+y,3/4+x", "1/4-z,3/4+y,1/4+x", "3/4-y,1/4+x,3/4+z", "1/4-y,3/4+x,1/4+z", "1/4-x,1/4-z,1/4-y", "3/4-x,3/4-z,3/4-y", "1/4-z,1/4-y,1/4-x", "3/4-z,3/4-y,3/4-x", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,3/4-z", "1/2-z,-x,1/2+y", "-z,1/2-x,+y", "1/2-y,-z,1/2+x", "-y,1/2-z,+x", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "1/2+z,1/2-x,-y", "+z,-x,1/2-y", "1/2+y,1/2-z,-x", "+y,-z,1/2-x", "1/2+x,1/2-y,-z", "+x,-y,1/2-z", "3/4+x,3/4-z,1/4+y", "1/4+x,1/4-z,3/4+y", "3/4+z,3/4-y,1/4+x", "1/4+z,1/4-y,3/4+x", "3/4+y,3/4-x,1/4+z", "1/4+y,1/4-x,3/4+z", "1/4+x,3/4+z,3/4-y", "3/4+x,1/4+z,1/4-y", "1/4+z,3/4+y,3/4-x", "3/4+z,1/4+y,1/4-x", "1/4+y,3/4+x,3/4-z", "3/4+y,1/4+x,1/4-z", "z,x,y", "1/2+z,1/2+x,1/2+y", "y,z,x", "1/2+y,1/2+z,1/2+x"]


hm_notation: P 42/n b c
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "y,x,1/2-z", "1/2+y,-x,1/2-z", "1/2-y,x,1/2+z", "1/2+x,-y,z", "1/2-x,y,-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "1/2+y,1/2+x,1/2+z", "1/2-y,1/2-x,1/2-z", "-y,1/2+x,1/2-z", "y,1/2-x,1/2+z", "-x,1/2+y,z", "x,1/2-y,-z", "-x,-y,-z"]


hm_notation: A m a a
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,-y,z", "1/2-x,1/2-y,1/2+z", "1/2+x,-y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,y,z", "-x,1/2+y,1/2+z", "x,-y,-z", "x,1/2-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P 63 %var1%
symmetry_xyz:
["x,y,z", "2/3+x-y,1/3+x,1/2+z", "-y,+x-y,z", "2/3-x,1/3-y,1/2+z", "-x+y,-x,z", "2/3+y,1/3-x+y,1/2+z"]


hm_notation: P b n n
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,1/2+y,z", "x,1/2-y,-z", "-x,-y,-z"]


hm_notation: B b a 2
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "1/2-x,1/2+y,z", "-x,1/2+y,1/2+z", "1/2+x,1/2-y,z", "+x,1/2-y,1/2+z", "-x,-y,z", "1/2-x,-y,1/2+z"]


hm_notation: I m c m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-x,y,z", "-x,1/2+y,1/2+z", "1/2+x,-y,-z", "+x,1/2-y,1/2-z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: C c m b %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/2-x,y,1/2+z", "-x,1/2+y,1/2+z", "1/2+x,-y,1/2-z", "+x,1/2-y,1/2-z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "1/2+x,y,1/2-z", "+x,1/2+y,1/2-z", "1/2-x,-y,1/2+z", "-x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: P m n m
symmetry_xyz:
["x,y,z", "1/2-x,y,z", "1/2+x,-y,-z", "x,y,1/2-z", "-x,-y,1/2+z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,-y,-z"]


hm_notation: F 1 1 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z"]


hm_notation: B b 21 m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "-x,1/2+y,z", "1/2-x,1/2+y,1/2+z", "x,y,-z", "1/2+x,y,1/2-z", "-x,1/2+y,-z", "1/2-x,1/2+y,1/2-z"]


hm_notation: B 1 1 2/m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "-x,-y,z", "1/2-x,-y,1/2+z", "x,y,-z", "1/2+x,y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: F d 3 c
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+z,-x,3/4+y", "3/4+z,1/2-x,1/4+y", "1/4+z,-x,1/4+y", "1/4+z,1/2-x,3/4+y", "3/4-y,1/2+z,1/4-x", "3/4-y,+z,3/4-x", "1/4-y,1/2+z,3/4-x", "1/4-y,+z,1/4-x", "1/4+x,1/2-y,3/4+z", "1/4+x,-y,1/4+z", "3/4+x,1/2-y,1/4+z", "3/4+x,-y,3/4+z", "3/4-z,x,3/4-y", "3/4-z,1/2+x,1/4-y", "1/4-z,x,1/4-y", "1/4-z,1/2+x,3/4-y", "3/4+y,1/2-z,1/4+x", "3/4+y,-z,3/4+x", "1/4+y,1/2-z,3/4+x", "1/4+y,-z,1/4+x", "1/4-x,1/2+y,3/4-z", "1/4-x,+y,1/4-z", "3/4-x,1/2+y,1/4-z", "3/4-x,+y,3/4-z", "1/2+x,1/4-z,1/4-y", "1/2+x,3/4-z,3/4-y", "+x,1/4-z,3/4-y", "+x,3/4-z,1/4-y", "-z,1/4+y,3/4+x", "-z,3/4+y,1/4+x", "1/2-z,1/4+y,1/4+x", "1/2-z,3/4+y,3/4+x", "y,3/4-x,1/4-z", "y,1/4-x,3/4-z", "1/2+y,3/4-x,3/4-z", "1/2+y,1/4-x,1/4-z", "1/2-x,1/4+z,1/4+y", "1/2-x,3/4+z,3/4+y", "-x,1/4+z,3/4+y", "-x,3/4+z,1/4+y", "z,1/4-y,3/4-x", "z,3/4-y,1/4-x", "1/2+z,1/4-y,1/4-x", "1/2+z,3/4-y,3/4-x", "-y,3/4+x,1/4+z", "-y,1/4+x,3/4+z", "1/2-y,3/4+x,3/4+z", "1/2-y,1/4+x,1/4+z", "x,1/2+z,y", "x,+z,1/2+y", "1/2+x,1/2+z,1/2+y", "1/2+x,+z,y", "1/2-z,1/2-y,1/2-x", "1/2-z,-y,-x", "-z,1/2-y,-x", "-z,-y,1/2-x", "1/2+y,x,z", "1/2+y,1/2+x,1/2+z", "+y,x,1/2+z", "+y,1/2+x,z", "-x,1/2-z,-y", "-x,-z,1/2-y", "1/2-x,1/2-z,1/2-y", "1/2-x,-z,-y", "1/2+z,1/2+y,1/2+x", "1/2+z,+y,+x", "+z,1/2+y,+x", "+z,+y,1/2+x", "1/2-y,-x,-z", "1/2-y,1/2-x,1/2-z", "-y,-x,1/2-z", "-y,1/2-x,-z", "3/4+z,1/4+x,1/2-y", "3/4+z,3/4+x,-y", "1/4+z,1/4+x,-y", "1/4+z,3/4+x,1/2-y", "3/4-y,3/4-z,x", "3/4-y,1/4-z,1/2+x", "1/4-y,3/4-z,1/2+x", "1/4-y,1/4-z,x", "1/4+x,3/4+y,1/2-z", "1/4+x,1/4+y,-z", "3/4+x,3/4+y,-z", "3/4+x,1/4+y,1/2-z", "3/4-z,1/4-x,1/2+y", "3/4-z,3/4-x,+y", "1/4-z,1/4-x,+y", "1/4-z,3/4-x,1/2+y", "3/4+y,3/4+z,-x", "3/4+y,1/4+z,1/2-x", "1/4+y,3/4+z,1/2-x", "1/4+y,1/4+z,-x", "1/4-x,3/4-y,1/2+z", "1/4-x,1/4-y,+z", "3/4-x,3/4-y,+z", "3/4-x,1/4-y,1/2+z", "1/2-z,3/4+x,1/4+y", "1/2-z,1/4+x,3/4+y", "-z,3/4+x,3/4+y", "-z,1/4+x,1/4+y", "1/2+y,1/4-z,3/4-x", "1/2+y,3/4-z,1/4-x", "+y,1/4-z,1/4-x", "+y,3/4-z,3/4-x", "-x,1/4+y,1/4+z", "-x,3/4+y,3/4+z", "1/2-x,1/4+y,3/4+z", "1/2-x,3/4+y,1/4+z", "1/2+z,3/4-x,1/4-y", "1/2+z,1/4-x,3/4-y", "+z,3/4-x,3/4-y", "+z,1/4-x,1/4-y", "1/2-y,1/4+z,3/4+x", "1/2-y,3/4+z,1/4+x", "-y,1/4+z,1/4+x", "-y,3/4+z,3/4+x", "x,1/4-y,1/4-z", "x,3/4-y,3/4-z", "1/2+x,1/4-y,3/4-z", "1/2+x,3/4-y,1/4-z", "3/4-x,1/2+z,3/4-y", "3/4-x,+z,1/4-y", "1/4-x,1/2+z,1/4-y", "1/4-x,+z,3/4-y", "1/4+z,1/2-y,1/4+x", "1/4+z,-y,3/4+x", "3/4+z,1/2-y,3/4+x", "3/4+z,-y,1/4+x", "1/4-y,x,3/4-z", "1/4-y,1/2+x,1/4-z", "3/4-y,x,1/4-z", "3/4-y,1/2+x,3/4-z", "3/4+x,1/2-z,3/4+y", "3/4+x,-z,1/4+y", "1/4+x,1/2-z,1/4+y", "1/4+x,-z,3/4+y", "1/4-z,1/2+y,1/4-x", "1/4-z,+y,3/4-x", "3/4-z,1/2+y,3/4-x", "3/4-z,+y,1/4-x", "1/4+y,-x,3/4+z", "1/4+y,1/2-x,1/4+z", "3/4+y,-x,1/4+z", "3/4+y,1/2-x,3/4+z", "1/4-x,1/4-z,1/2+y", "1/4-x,3/4-z,+y", "3/4-x,1/4-z,+y", "3/4-x,3/4-z,1/2+y", "3/4+z,1/4+y,-x", "3/4+z,3/4+y,1/2-x", "1/4+z,1/4+y,1/2-x", "1/4+z,3/4+y,-x", "3/4-y,3/4-x,1/2+z", "3/4-y,1/4-x,+z", "1/4-y,3/4-x,+z", "1/4-y,1/4-x,1/2+z", "1/4+x,1/4+z,1/2-y", "1/4+x,3/4+z,-y", "3/4+x,1/4+z,-y", "3/4+x,3/4+z,1/2-y", "3/4-z,1/4-y,x", "3/4-z,3/4-y,1/2+x", "1/4-z,1/4-y,1/2+x", "1/4-z,3/4-y,x", "3/4+y,3/4+x,1/2-z", "3/4+y,1/4+x,-z", "1/4+y,3/4+x,-z", "1/4+y,1/4+x,1/2-z", "1/2-z,1/2-x,-y", "1/2-z,-x,1/2-y", "-z,1/2-x,1/2-y", "-z,-x,-y", "1/2+y,z,1/2+x", "1/2+y,1/2+z,+x", "+y,z,+x", "+y,1/2+z,1/2+x", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "1/2+z,1/2+x,y", "1/2+z,+x,1/2+y", "+z,1/2+x,1/2+y", "+z,+x,y", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x", "-y,-z,-x", "-y,1/2-z,1/2-x"]


hm_notation: P 42/n %var1%
symmetry_xyz:
["x,y,z", "y,-x,-z", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "-y,x,-z", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P b c b
symmetry_xyz:
["x,y,z", "-x,1/2+y,z", "x,1/2-y,-z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "x,-y,1/2+z", "-x,y,1/2-z", "-x,-y,-z"]


hm_notation: P n c m
symmetry_xyz:
["x,y,z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "x,y,-z", "-x,-y,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "-x,-y,-z"]


hm_notation: C -4 2 b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/2+y,x,z", "+y,1/2+x,z", "1/2-x,y,-z", "-x,1/2+y,-z", "1/2-y,-x,z", "-y,1/2-x,z", "1/2+x,-y,-z", "+x,1/2-y,-z", "y,-x,-z", "1/2+y,1/2-x,-z", "-x,-y,z", "1/2-x,1/2-y,z", "-y,x,-z", "1/2-y,1/2+x,-z"]


hm_notation: P n 3 m
symmetry_xyz:
["x,y,z", "1/2+z,1/2-x,1/2+y", "-y,z,-x", "1/2+x,1/2-y,1/2+z", "-z,x,-y", "1/2+y,1/2-z,1/2+x", "-x,y,-z", "x,-z,-y", "1/2-z,1/2+y,1/2+x", "y,-x,-z", "1/2-x,1/2+z,1/2+y", "z,-y,-x", "1/2-y,1/2+x,1/2+z", "x,z,y", "1/2-z,1/2-y,1/2-x", "y,x,z", "1/2-x,1/2-z,1/2-y", "z,y,x", "1/2-y,1/2-x,1/2-z", "1/2+z,1/2+x,1/2-y", "-y,-z,x", "1/2+x,1/2+y,1/2-z", "-z,-x,y", "1/2+y,1/2+z,1/2-x", "-x,-y,z", "1/2-z,1/2+x,1/2+y", "y,-z,-x", "1/2-x,1/2+y,1/2+z", "z,-x,-y", "1/2-y,1/2+z,1/2+x", "x,-y,-z", "-x,z,-y", "1/2+z,1/2-y,1/2+x", "-y,x,-z", "1/2+x,1/2-z,1/2+y", "-z,y,-x", "1/2+y,1/2-x,1/2+z", "-x,-z,y", "1/2+z,1/2+y,1/2-x", "-y,-x,z", "1/2+x,1/2+z,1/2-y", "-z,-y,x", "1/2+y,1/2+x,1/2-z", "1/2-z,1/2-x,1/2-y", "y,z,x", "1/2-x,1/2-y,1/2-z", "z,x,y", "1/2-y,1/2-z,1/2-x"]


hm_notation: P n 3 m %var1%
symmetry_xyz:
["x,y,z", "1/2+z,-x,1/2+y", "1/2-y,z,1/2-x", "1/2+x,-y,1/2+z", "1/2-z,x,1/2-y", "1/2+y,-z,1/2+x", "1/2-x,y,1/2-z", "x,1/2-z,1/2-y", "-z,1/2+y,1/2+x", "y,1/2-x,1/2-z", "-x,1/2+z,1/2+y", "z,1/2-y,1/2-x", "-y,1/2+x,1/2+z", "x,z,y", "-z,-y,-x", "y,x,z", "-x,-z,-y", "z,y,x", "-y,-x,-z", "1/2+z,1/2+x,-y", "1/2-y,1/2-z,x", "1/2+x,1/2+y,-z", "1/2-z,1/2-x,y", "1/2+y,1/2+z,-x", "1/2-x,1/2-y,z", "-z,1/2+x,1/2+y", "y,1/2-z,1/2-x", "-x,1/2+y,1/2+z", "z,1/2-x,1/2-y", "-y,1/2+z,1/2+x", "x,1/2-y,1/2-z", "1/2-x,z,1/2-y", "1/2+z,-y,1/2+x", "1/2-y,x,1/2-z", "1/2+x,-z,1/2+y", "1/2-z,y,1/2-x", "1/2+y,-x,1/2+z", "1/2-x,1/2-z,y", "1/2+z,1/2+y,-x", "1/2-y,1/2-x,z", "1/2+x,1/2+z,-y", "1/2-z,1/2-y,x", "1/2+y,1/2+x,-z", "-z,-x,-y", "y,z,x", "-x,-y,-z", "z,x,y", "-y,-z,-x"]


hm_notation: C c m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,1/2+z", "1/2-x,1/2+y,1/2+z", "x,-y,1/2-z", "1/2+x,1/2-y,1/2-z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "x,y,1/2-z", "1/2+x,1/2+y,1/2-z", "-x,-y,1/2+z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: F m 2 m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z"]


hm_notation: F m 3
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "z,x,-y", "z,1/2+x,1/2-y", "1/2+z,x,1/2-y", "1/2+z,1/2+x,-y", "z,-x,y", "z,1/2-x,1/2+y", "1/2+z,-x,1/2+y", "1/2+z,1/2-x,y", "-z,x,y", "-z,1/2+x,1/2+y", "1/2-z,x,1/2+y", "1/2-z,1/2+x,y", "-z,-x,-y", "-z,1/2-x,1/2-y", "1/2-z,-x,1/2-y", "1/2-z,1/2-x,-y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "-y,z,x", "-y,1/2+z,1/2+x", "1/2-y,z,1/2+x", "1/2-y,1/2+z,x", "y,z,-x", "y,1/2+z,1/2-x", "1/2+y,z,1/2-x", "1/2+y,1/2+z,-x", "y,-z,x", "y,1/2-z,1/2+x", "1/2+y,-z,1/2+x", "1/2+y,1/2-z,x", "-y,-z,-x", "-y,1/2-z,1/2-x", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z"]


hm_notation: P b a n %var1%
symmetry_xyz:
["x,y,z", "1/2+x,-y,z", "1/2-x,y,-z", "-x,1/2+y,z", "x,1/2-y,-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-x,-y,-z"]


hm_notation: P n 3 n
symmetry_xyz:
["x,y,z", "1/2+z,1/2-x,1/2+y", "-y,z,-x", "1/2+x,1/2-y,1/2+z", "-z,x,-y", "1/2+y,1/2-z,1/2+x", "-x,y,-z", "1/2+x,1/2-z,1/2-y", "-z,y,x", "1/2+y,1/2-x,1/2-z", "-x,z,y", "1/2+z,1/2-y,1/2-x", "-y,x,z", "1/2+x,1/2+z,1/2+y", "-z,-y,-x", "1/2+y,1/2+x,1/2+z", "-x,-z,-y", "1/2+z,1/2+y,1/2+x", "-y,-x,-z", "1/2+z,1/2+x,1/2-y", "-y,-z,x", "1/2+x,1/2+y,1/2-z", "-z,-x,y", "1/2+y,1/2+z,1/2-x", "-x,-y,z", "1/2-z,1/2+x,1/2+y", "y,-z,-x", "1/2-x,1/2+y,1/2+z", "z,-x,-y", "1/2-y,1/2+z,1/2+x", "x,-y,-z", "1/2-x,1/2+z,1/2-y", "z,-y,x", "1/2-y,1/2+x,1/2-z", "x,-z,y", "1/2-z,1/2+y,1/2-x", "y,-x,z", "1/2-x,1/2-z,1/2+y", "z,y,-x", "1/2-y,1/2-x,1/2+z", "x,z,-y", "1/2-z,1/2-y,1/2+x", "y,x,-z", "1/2-z,1/2-x,1/2-y", "y,z,x", "1/2-x,1/2-y,1/2-z", "z,x,y", "1/2-y,1/2-z,1/2-x"]


hm_notation: C m 2 m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,z", "1/2-x,1/2+y,z", "x,y,-z", "1/2+x,1/2+y,-z", "-x,y,-z", "1/2-x,1/2+y,-z"]


hm_notation: P m a n
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-x,y,z", "x,-y,-z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "-x,-y,-z"]


hm_notation: P 4/n b m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "y,x,-z", "1/2+y,1/2-x,-z", "-y,x,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2+y,1/2+x,z", "-y,-x,-z", "1/2-y,1/2+x,-z", "y,-x,z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: F 1 2/m 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: B 1 1 21/d
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "3/4-x,3/4-y,1/2+z", "1/4-x,3/4-y,+z", "3/4+x,3/4+y,1/2-z", "1/4+x,3/4+y,-z", "1/2-x,1/2-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P 6/m
symmetry_xyz:
["x,y,z", "-x+y,-x,-z", "x-y,x,z", "y,-x+y,-z", "-y,x-y,z", "x,y,-z", "-x,-y,z", "x-y,x,-z", "-x+y,-x,z", "-y,x-y,-z", "y,-x+y,z", "-x,-y,-z"]


hm_notation: P 42/n c m %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "y,x,1/2-z", "y,-x,-z", "1/2-y,1/2+x,1/2+z", "x,-y,1/2+z", "1/2-x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2+y,1/2+x,z", "-y,-x,1/2-z", "-y,x,-z", "1/2+y,1/2-x,1/2+z", "-x,y,1/2+z", "1/2+x,1/2-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P 42 3 2
symmetry_xyz:
["x,y,z", "-z,x,-y", "-y,z,-x", "-x,y,-z", "1/2-x,1/2+z,1/2+y", "1/2-z,1/2+y,1/2+x", "1/2-y,1/2+x,1/2+z", "1/2-x,1/2-z,1/2-y", "1/2-z,1/2-y,1/2-x", "1/2-y,1/2-x,1/2-z", "-z,-x,y", "-y,-z,x", "-x,-y,z", "z,-x,-y", "y,-z,-x", "x,-y,-z", "1/2+x,1/2-z,1/2+y", "1/2+z,1/2-y,1/2+x", "1/2+y,1/2-x,1/2+z", "1/2+x,1/2+z,1/2-y", "1/2+z,1/2+y,1/2-x", "1/2+y,1/2+x,1/2-z", "z,x,y", "y,z,x"]


hm_notation: P 4/n n c %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "y,x,-z", "1/2+y,1/2-x,1/2-z", "-y,x,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "-y,-x,-z", "1/2-y,1/2+x,1/2-z", "y,-x,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I c m a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,1/2+y,z", "1/2-x,+y,1/2+z", "x,1/2-y,-z", "1/2+x,-y,1/2-z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "-x,1/2-y,z", "1/2-x,-y,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P m n m %var1%
symmetry_xyz:
["x,y,z", "-x,y,z", "1/2+x,-y,1/2-z", "x,y,-z", "1/2-x,-y,1/2+z", "1/2+x,-y,1/2+z", "-x,y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P c m b
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "-x,y,1/2+z", "x,-y,1/2-z", "x,1/2-y,z", "-x,1/2+y,-z", "-x,-y,-z"]


hm_notation: P m c n %var1%
symmetry_xyz:
["x,y,z", "-x,y,z", "1/2+x,1/2-y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,1/2+z", "x,-y,1/2+z", "1/2-x,1/2+y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: I 2 m b %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "x,1/2-y,z", "1/2+x,-y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: P m c n %var2%
symmetry_xyz:
["x,y,z", "-x,y,z", "1/2+x,-y,1/2-z", "1/2+x,1/2+y,-z", "-x,1/2-y,1/2+z", "x,1/2-y,1/2+z", "1/2-x,1/2+y,-z", "1/2-x,-y,1/2-z"]


hm_notation: I 1 2/a 1 %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "1/2-x,-y,1/2-z", "-x,1/2-y,-z"]


hm_notation: A 1 1 2/m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,y,-z", "x,1/2+y,1/2-z", "-x,-y,z", "-x,1/2-y,1/2+z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: C c c 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,1/2+z", "1/2-x,1/2+y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,z"]


hm_notation: I b m 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,1/2+y,z", "1/2-x,+y,1/2+z", "x,1/2-y,z", "1/2+x,-y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: I m c b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+x,y,-z", "+x,1/2+y,1/2-z", "1/2-x,-y,z", "-x,1/2-y,1/2+z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 1 2/m 1 %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2-y,z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,1/2+y,-z", "1/2-x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: A 1 2/a 1 %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,1/2-y,z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: P 42/n m c %var2%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,1/2-z", "1/2+y,-x,1/2-z", "1/2-y,x,1/2+z", "x,1/2-y,z", "-x,1/2+y,-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,1/2+x,1/2-z", "y,1/2-x,1/2+z", "1/2-x,y,z", "1/2+x,-y,-z", "-x,-y,-z"]


hm_notation: P n m b
symmetry_xyz:
["x,y,z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "x,-y,z", "-x,y,-z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "-x,-y,-z"]


hm_notation: P c n b
symmetry_xyz:
["x,y,z", "x,1/2+y,-z", "-x,1/2-y,z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z"]


hm_notation: P 6 2 2
symmetry_xyz:
["x,y,z", "x,x-y,-z", "x-y,x,z", "y,x,-z", "-y,x-y,z", "-x+y,y,-z", "-x,-y,z", "-x,-x+y,-z", "-x+y,-x,z", "-y,-x,-z", "y,-x+y,z", "x-y,-y,-z"]


hm_notation: P 4 21 2 %var1%
symmetry_xyz:
["x,y,z", "1/2+y,1/2+x,-z", "1/2-y,x,z", "-x,1/2+y,-z", "1/2-x,1/2-y,z", "-y,-x,-z", "y,1/2-x,z", "1/2+x,-y,-z"]


hm_notation: F d 3 c %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+z,3/4-x,3/4+y", "3/4+z,1/4-x,1/4+y", "1/4+z,3/4-x,1/4+y", "1/4+z,1/4-x,3/4+y", "1/2-y,1/2+z,-x", "1/2-y,+z,1/2-x", "-y,1/2+z,1/2-x", "-y,+z,-x", "1/4+x,1/4-y,3/4+z", "1/4+x,3/4-y,1/4+z", "3/4+x,1/4-y,1/4+z", "3/4+x,3/4-y,3/4+z", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "-z,x,-y", "-z,1/2+x,1/2-y", "3/4+y,1/4-z,1/4+x", "3/4+y,3/4-z,3/4+x", "1/4+y,1/4-z,3/4+x", "1/4+y,3/4-z,1/4+x", "-x,1/2+y,1/2-z", "-x,+y,-z", "1/2-x,1/2+y,-z", "1/2-x,+y,1/2-z", "1/2+x,-z,-y", "1/2+x,1/2-z,1/2-y", "+x,-z,1/2-y", "+x,1/2-z,-y", "3/4-z,1/4+y,3/4+x", "3/4-z,3/4+y,1/4+x", "1/4-z,1/4+y,1/4+x", "1/4-z,3/4+y,3/4+x", "y,1/2-x,-z", "y,-x,1/2-z", "1/2+y,1/2-x,1/2-z", "1/2+y,-x,-z", "1/4-x,1/4+z,1/4+y", "1/4-x,3/4+z,3/4+y", "3/4-x,1/4+z,3/4+y", "3/4-x,3/4+z,1/4+y", "z,-y,1/2-x", "z,1/2-y,-x", "1/2+z,-y,-x", "1/2+z,1/2-y,1/2-x", "3/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/4-y,3/4+x,3/4+z", "1/4-y,1/4+x,1/4+z", "x,1/2+z,y", "x,+z,1/2+y", "1/2+x,1/2+z,1/2+y", "1/2+x,+z,y", "1/4-z,1/4-y,1/4-x", "1/4-z,3/4-y,3/4-x", "3/4-z,1/4-y,3/4-x", "3/4-z,3/4-y,1/4-x", "1/2+y,x,z", "1/2+y,1/2+x,1/2+z", "+y,x,1/2+z", "+y,1/2+x,z", "3/4-x,1/4-z,3/4-y", "3/4-x,3/4-z,1/4-y", "1/4-x,1/4-z,1/4-y", "1/4-x,3/4-z,3/4-y", "1/2+z,1/2+y,1/2+x", "1/2+z,+y,+x", "+z,1/2+y,+x", "+z,+y,1/2+x", "1/4-y,3/4-x,3/4-z", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,1/4-z", "3/4-y,1/4-x,3/4-z", "3/4+z,1/4+x,1/4-y", "3/4+z,3/4+x,3/4-y", "1/4+z,1/4+x,3/4-y", "1/4+z,3/4+x,1/4-y", "1/2-y,1/2-z,x", "1/2-y,-z,1/2+x", "-y,1/2-z,1/2+x", "-y,-z,x", "1/4+x,3/4+y,1/4-z", "1/4+x,1/4+y,3/4-z", "3/4+x,3/4+y,3/4-z", "3/4+x,1/4+y,1/4-z", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,+y", "-z,-x,+y", "-z,1/2-x,1/2+y", "3/4+y,3/4+z,3/4-x", "3/4+y,1/4+z,1/4-x", "1/4+y,3/4+z,1/4-x", "1/4+y,1/4+z,3/4-x", "-x,1/2-y,1/2+z", "-x,-y,+z", "1/2-x,1/2-y,+z", "1/2-x,-y,1/2+z", "1/4-z,3/4+x,1/4+y", "1/4-z,1/4+x,3/4+y", "3/4-z,3/4+x,3/4+y", "3/4-z,1/4+x,1/4+y", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "+y,-z,-x", "+y,1/2-z,1/2-x", "3/4-x,1/4+y,1/4+z", "3/4-x,3/4+y,3/4+z", "1/4-x,1/4+y,3/4+z", "1/4-x,3/4+y,1/4+z", "1/2+z,1/2-x,-y", "1/2+z,-x,1/2-y", "+z,1/2-x,1/2-y", "+z,-x,-y", "1/4-y,1/4+z,3/4+x", "1/4-y,3/4+z,1/4+x", "3/4-y,1/4+z,1/4+x", "3/4-y,3/4+z,3/4+x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "1/2-x,1/2+z,1/2-y", "1/2-x,+z,-y", "-x,1/2+z,-y", "-x,+z,1/2-y", "1/4+z,1/4-y,1/4+x", "1/4+z,3/4-y,3/4+x", "3/4+z,1/4-y,3/4+x", "3/4+z,3/4-y,1/4+x", "-y,x,1/2-z", "-y,1/2+x,-z", "1/2-y,x,-z", "1/2-y,1/2+x,1/2-z", "3/4+x,1/4-z,3/4+y", "3/4+x,3/4-z,1/4+y", "1/4+x,1/4-z,1/4+y", "1/4+x,3/4-z,3/4+y", "-z,1/2+y,-x", "-z,+y,1/2-x", "1/2-z,1/2+y,1/2-x", "1/2-z,+y,-x", "1/4+y,3/4-x,3/4+z", "1/4+y,1/4-x,1/4+z", "3/4+y,3/4-x,1/4+z", "3/4+y,1/4-x,3/4+z", "-x,-z,1/2+y", "-x,1/2-z,+y", "1/2-x,-z,+y", "1/2-x,1/2-z,1/2+y", "3/4+z,1/4+y,3/4-x", "3/4+z,3/4+y,1/4-x", "1/4+z,1/4+y,1/4-x", "1/4+z,3/4+y,3/4-x", "1/2-y,1/2-x,1/2+z", "1/2-y,-x,+z", "-y,1/2-x,+z", "-y,-x,1/2+z", "1/4+x,1/4+z,1/4-y", "1/4+x,3/4+z,3/4-y", "3/4+x,1/4+z,3/4-y", "3/4+x,3/4+z,1/4-y", "1/2-z,-y,x", "1/2-z,1/2-y,1/2+x", "-z,-y,1/2+x", "-z,1/2-y,x", "3/4+y,3/4+x,1/4-z", "3/4+y,1/4+x,3/4-z", "1/4+y,3/4+x,3/4-z", "1/4+y,1/4+x,1/4-z", "1/4-z,1/4-x,3/4-y", "1/4-z,3/4-x,1/4-y", "3/4-z,1/4-x,1/4-y", "3/4-z,3/4-x,3/4-y", "1/2+y,z,1/2+x", "1/2+y,1/2+z,+x", "+y,z,+x", "+y,1/2+z,1/2+x", "3/4-x,3/4-y,3/4-z", "3/4-x,1/4-y,1/4-z", "1/4-x,3/4-y,1/4-z", "1/4-x,1/4-y,3/4-z", "1/2+z,1/2+x,y", "1/2+z,+x,1/2+y", "+z,1/2+x,1/2+y", "+z,+x,y", "1/4-y,3/4-z,1/4-x", "1/4-y,1/4-z,3/4-x", "3/4-y,3/4-z,3/4-x", "3/4-y,1/4-z,1/4-x"]


hm_notation: I b m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,y,1/2-z", "1/2+x,1/2+y,-z", "-x,-y,1/2+z", "1/2-x,1/2-y,+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P 4 n c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "-y,x,z", "1/2+x,1/2-y,1/2+z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "y,-x,z", "1/2-x,1/2+y,1/2+z"]


hm_notation: F 2 m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z"]


hm_notation: C m c m %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,1/2+y,1/2-z", "1/2-x,y,z", "-x,1/2+y,z", "x,1/2-y,-z", "1/2+x,-y,-z", "x,y,1/2-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "-x,-y,1/2+z", "1/2-x,1/2-y,-z", "-x,-y,-z"]


hm_notation: I 1 2/a 1 %var2%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "1/2+x,1/2-y,z", "+x,-y,1/2+z", "1/2-x,1/2-y,-z", "-x,-y,1/2-z"]


hm_notation: I m a b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+x,y,-z", "+x,1/2+y,1/2-z", "1/2-x,-y,z", "-x,1/2-y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P 42/n b c %var1%
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "1/2+y,1/2+x,1/2-z", "y,-x,1/2-z", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "y,x,1/2+z", "1/2-y,1/2-x,1/2-z", "-y,x,1/2-z", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: F 1 2/d 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,-y,1/4+z", "1/4+x,1/2-y,3/4+z", "3/4+x,-y,3/4+z", "3/4+x,1/2-y,1/4+z", "3/4-x,y,3/4-z", "3/4-x,1/2+y,1/4-z", "1/4-x,y,1/4-z", "1/4-x,1/2+y,3/4-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P 64 2 2
symmetry_xyz:
["x,y,z", "x,x-y,2/3-z", "x-y,x,2/3+z", "y,x,1/3-z", "-y,x-y,1/3+z", "-x+y,y,-z", "-x,-y,z", "-x,-x+y,2/3-z", "-x+y,-x,2/3+z", "-y,-x,1/3-z", "y,-x+y,1/3+z", "x-y,-y,-z"]


hm_notation: C 1 1 2/a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/2+x,y,-z", "+x,1/2+y,-z", "1/2-x,-y,z", "-x,1/2-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: A 21 2 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2-x,-y,z", "1/2-x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: P 65 2 2
symmetry_xyz:
["x,y,z", "x,x-y,5/6-z", "x-y,x,5/6+z", "y,x,2/3-z", "-y,x-y,2/3+z", "-x+y,y,1/2-z", "-x,-y,1/2+z", "-x,-x+y,1/3-z", "-x+y,-x,1/3+z", "-y,-x,1/6-z", "y,-x+y,1/6+z", "x-y,-y,-z"]


hm_notation: F 1 d 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,-y,1/4+z", "1/4+x,1/2-y,3/4+z", "3/4+x,-y,3/4+z", "3/4+x,1/2-y,1/4+z"]


hm_notation: F 1 2/d 1 %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,-y,1/4+z", "1/4+x,1/2-y,3/4+z", "3/4+x,-y,3/4+z", "3/4+x,1/2-y,1/4+z", "3/4-x,y,1/4-z", "3/4-x,1/2+y,3/4-z", "1/4-x,y,3/4-z", "1/4-x,1/2+y,1/4-z", "1/2-x,-y,-z", "1/2-x,1/2-y,1/2-z", "-x,-y,1/2-z", "-x,1/2-y,-z"]


hm_notation: A 1 2/n 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: F 2 d d
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,1/4+y,1/4-z", "1/4+x,3/4+y,3/4-z", "3/4+x,1/4+y,3/4-z", "3/4+x,3/4+y,1/4-z", "1/4+x,1/4-y,1/4+z", "1/4+x,3/4-y,3/4+z", "3/4+x,1/4-y,3/4+z", "3/4+x,3/4-y,1/4+z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "+x,-y,-z", "+x,1/2-y,1/2-z"]


hm_notation: B b c m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "1/2-x,1/2+y,z", "-x,1/2+y,1/2+z", "1/2+x,1/2-y,-z", "+x,1/2-y,1/2-z", "x,y,-z", "1/2+x,y,1/2-z", "-x,-y,z", "1/2-x,-y,1/2+z", "1/2+x,1/2-y,z", "+x,1/2-y,1/2+z", "1/2-x,1/2+y,-z", "-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P b n b
symmetry_xyz:
["x,y,z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,-y,-z"]


hm_notation: C m m b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,1/2+y,z", "1/2-x,+y,z", "x,1/2-y,-z", "1/2+x,-y,-z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "x,1/2+y,-z", "1/2+x,+y,-z", "-x,1/2-y,z", "1/2-x,-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: A b m a
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,+z", "x,-y,z", "x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,+z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: I b a 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: A 21 a m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,-y,z", "1/2+x,1/2-y,1/2+z", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: P n a b
symmetry_xyz:
["x,y,z", "1/2+x,-y,z", "1/2-x,y,-z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: A 21 m a
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,-z", "1/2+x,1/2+y,1/2-z", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: F 1 d 1 %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,1/4-y,1/4+z", "1/4+x,3/4-y,3/4+z", "3/4+x,1/4-y,3/4+z", "3/4+x,3/4-y,1/4+z"]


hm_notation: B 1 21/m 1
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "x,1/2-y,z", "1/2+x,1/2-y,1/2+z", "-x,1/2+y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P b a a
symmetry_xyz:
["x,y,z", "1/2+x,y,-z", "1/2-x,-y,z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "-x,1/2+y,z", "x,1/2-y,-z", "-x,-y,-z"]


hm_notation: P 21 3 %var1%
symmetry_xyz:
["x,y,z", "-z,1/2-x,1/2+y", "1/2-z,1/2+x,-y", "1/2+z,-x,1/2-y", "z,x,y", "1/2+y,-z,1/2-x", "-y,1/2-z,1/2+x", "1/2-y,1/2+z,-x", "y,z,x", "1/2-x,1/2+y,-z", "1/2+x,-y,1/2-z", "-x,1/2-y,1/2+z"]


hm_notation: I m a 2 %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "1/2-x,y,z", "-x,1/2+y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: I 21 21 21 %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "1/2+x,1/2-y,-z", "+x,-y,1/2-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z"]


hm_notation: P 62 2 2 %var1%
symmetry_xyz:
["x,y,z", "x,x-y,-z", "x-y,x,1/3+z", "y,x,1/3-z", "-y,x-y,2/3+z", "-x+y,y,2/3-z", "-x,-y,z", "-x,-x+y,-z", "-x+y,-x,1/3+z", "-y,-x,1/3-z", "y,-x+y,2/3+z", "x-y,-y,2/3-z"]


hm_notation: F -4 d 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+y,1/4+x,3/4-z", "1/4+y,3/4+x,1/4-z", "3/4+y,1/4+x,1/4-z", "3/4+y,3/4+x,3/4-z", "1/4-x,1/4+y,3/4+z", "1/4-x,3/4+y,1/4+z", "3/4-x,1/4+y,1/4+z", "3/4-x,3/4+y,3/4+z", "1/4-y,1/4-x,3/4-z", "1/4-y,3/4-x,1/4-z", "3/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,3/4-z", "1/4+x,1/4-y,3/4+z", "1/4+x,3/4-y,1/4+z", "3/4+x,1/4-y,1/4+z", "3/4+x,3/4-y,3/4+z", "1/2+y,-x,1/2-z", "1/2+y,1/2-x,-z", "+y,-x,-z", "+y,1/2-x,1/2-z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,+z", "-x,-y,+z", "-x,1/2-y,1/2+z", "1/2-y,x,1/2-z", "1/2-y,1/2+x,-z", "-y,x,-z", "-y,1/2+x,1/2-z"]


hm_notation: P 42/m m c %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,1/2-z", "1/2+y,1/2-x,1/2-z", "1/2-y,1/2+x,1/2+z", "x,-y,z", "-x,y,-z", "x,y,-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "1/2-y,1/2-x,1/2-z", "1/2-y,1/2+x,1/2-z", "1/2+y,1/2-x,1/2+z", "-x,y,z", "x,-y,-z", "-x,-y,-z"]


hm_notation: I 1 2/c 1 %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2-y,1/2+z", "1/2+x,-y,+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,1/2-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: I 41 c d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,1/2-x,3/4+z", "1/2-y,-x,1/4+z", "-y,1/2+x,1/4+z", "1/2-y,+x,3/4+z", "1/2+x,1/2-y,z", "+x,-y,1/2+z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z", "1/2+y,x,1/4+z", "+y,1/2+x,3/4+z", "1/2+y,-x,3/4+z", "+y,1/2-x,1/4+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z"]


hm_notation: P 4 3 2
symmetry_xyz:
["x,y,z", "-z,x,-y", "-y,z,-x", "-x,y,-z", "-x,z,y", "-z,y,x", "-y,x,z", "-x,-z,-y", "-z,-y,-x", "-y,-x,-z", "-z,-x,y", "-y,-z,x", "-x,-y,z", "z,-x,-y", "y,-z,-x", "x,-y,-z", "x,-z,y", "z,-y,x", "y,-x,z", "x,z,-y", "z,y,-x", "y,x,-z", "z,x,y", "y,z,x"]


hm_notation: C 2 c b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "x,1/2+y,1/2-z", "1/2+x,+y,1/2-z", "x,-y,-z", "1/2+x,1/2-y,-z"]


hm_notation: I 2 m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z"]


# cif

formula: Na.09 Ca.616 Mg.902 Fe.21 Al.342 Ti.02 Si1.82 O6
compound: Kakanui, New Zealand
formula_title: <missing>
a: 9.699
b: 8.844
c: 5.272
alpha: 90
beta: 106.97
gamma: 90
cell_volume: 432.531
crystal_density: 3.343
atoms_sites: ["Na1", "Ca1", "Mg1", "Mg2", "Fe1", "Fe2", "Al1", "Al2", "Ti1", "Si1", "O1", "O2", "O3"]
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pub_title:
 Crystal-chemical characterization of clinopyroxenes based on eight new
 structure refinements
 _cod_database_code 1000035

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formula: (Fe6.1 Mg.9) Si8 O23.5 (F.5 H1.5)
compound: Wabush iron formation, Labrador, Canada
pub_title: The crystal structure and cation distribution of a grunerite
formula_title: <missing>
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c: 5.3388
alpha: 90
beta: 101.892
gamma: 90
cell_volume: 919.015
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atoms_aniso_label:
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formula: Pb S
compound: Colorado, USA
pub_title: The crystal structures of some metallic sulfides
formula_title: <missing>
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alpha: 90
beta: 90
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formula: Pb Se
compound: Synthetic
pub_title: The crystal structures of some metallic sulfides
formula_title: <missing>
a: 6.14
b: 6.14
c: 6.14
alpha: 90
beta: 90
gamma: 90
cell_volume: 231.476
crystal_density: 8.211
atoms_sites: ["Pb", "Se"]
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formula: Pb Te
compound: Synthetic
pub_title: The crystal structures of some metallic sulfides
formula_title: <missing>
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c: 6.34
alpha: 90
beta: 90
gamma: 90
cell_volume: 254.840
crystal_density: 8.726
atoms_sites: ["Pb", "Te"]
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qdat:
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formula: Fe S2
compound: natural, unknown
pub_title: The crystal structures of some metallic sulfides
formula_title: <missing>
a: 5.38
b: 5.38
c: 5.38
alpha: 90
beta: 90
gamma: 90
cell_volume: 155.721
crystal_density: 5.118
atoms_sites: ["Fe", "S"]
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formula: Hg S
compound: unknown
pub_title: The crystal structures of some metallic sulfides
formula_title: <missing>
a: 4.15
b: 4.15
c: 9.51
alpha: 90
beta: 90
gamma: 120
cell_volume: 141.843
crystal_density: 8.171
atoms_sites: ["Hg", "S"]
atoms_x: VVgUAFVYFAA=
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formula: Fe S2
compound: Joplin, Missouri, USA
pub_title: The crystal structure of marcasite
formula_title: <missing>
a: 3.37
b: 4.44
c: 5.39
alpha: 90
beta: 90
gamma: 90
cell_volume: 80.649
crystal_density: 4.941
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qdat:
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formula: S K O3
compound: <missing>
formula_title: K2S2O6
a: 9.82
b: 9.82
c: 6.36
alpha: 90
beta: 90
gamma: 120
cell_volume: 531.142
crystal_density: 2.235
atoms_sites: ["S1", "S2", "S3", "K1", "K2", "O1", "O2", "O3"]
atoms_x: AAAAAFVYFABVWBQAYOMWAEAdKgAgEgoAYIklAKDSHgA=
atoms_y: AAAAAKuwKACrsCgAYOMWAEAdKgDAtgYAQGAKAEDRDAA=
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atoms_aniso_u22: 0
atoms_aniso_u33: 0
atoms_aniso_u12: 0
atoms_aniso_u13: 0
atoms_aniso_u23: 0
pub_title:
 The crystal structure of potassium dithionate, K2S2O6
 Note: coordinates revised according to Am Min 18 (1933) 455-457

qdat:
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formula: S Rb O3
compound: <missing>
pub_title: The crystal structure of potassium dithionate, K2S2O6
formula_title: Rb2S2O6
a: 10.0
b: 10.0
c: 6.3
alpha: 90
beta: 90
gamma: 120
cell_volume: 545.596
crystal_density: 3.023
atoms_sites: ["S1", "S2", "S3", "Rb1", "Rb2", "O1", "O2", "O3"]
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qdat:
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formula: Cu.53 Fe.31 Zn.01 Sn.05 Mo.09 S.71 As.03 Te.02 Sb.01
compound: Leonard mine, Butte, Montana, USA
pub_title: X-Ray examination of colusite, (Cu,Fe,Mo,Sn)4(S,As,Te)3-4
formula_title: <missing>
a: 5.304
b: 5.304
c: 5.304
alpha: 90
beta: 90
gamma: 90
cell_volume: 149.214
crystal_density: 4.229
atoms_sites: ["Cu", "Fe", "Zn", "Sn", "Mo", "S", "As", "Te", "Sb"]
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qdat:
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formula: Mg3 Si4 (O12 H2)
compound: Structure results from data of many samples
pub_title: The structures of vermiculites and their collapse by dehydration
formula_title: <missing>
a: 5.31
b: 9.20
c: 28.46
alpha: 90
beta: 97.14
gamma: 90
cell_volume: 1379.547
crystal_density: 1.826
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atoms_sites:
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qdat:
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formula: Sb Na Be4 O7
compound: not given
pub_title: The crystal structure of swedenborgite, NaBe4SbO7
formula_title: <missing>
a: 5.47
b: 5.47
c: 8.92
alpha: 90
beta: 90
gamma: 120
cell_volume: 231.137
crystal_density: 4.207
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qdat:
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formula: Fe Sb2 S4
compound: <missing>
pub_title: The crystal structure of berthierite
formula_title: <missing>
a: 11.44
b: 14.12
c: 3.76
alpha: 90
beta: 90
gamma: 90
cell_volume: 607.363
crystal_density: 4.676
atoms_sites: ["Fe", "Sb1", "Sb2", "S1", "S2", "S3", "S4"]
atoms_x: kNADALBxCwCwcQsAkNADALBxCwCwcQsAkNADAA==
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formula: Sb2 O3
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pub_title: The crystal structure of valentinite
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formula: K S2 Al3 O14 H6
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pub_title: The crystal structures of alunite and the jarosites
formula_title: <missing>
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pub_title: The crystal structure of plazolite
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formula: Fe Sb S
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formula: Si.5 Fe1.4 O4.001 H1.667
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formula_title: <missing>
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pub_title:
 Random structures of layer minerals as illustrated by cronstedtite
 (2FeO.Fe2O3.SiO2.2H2O). Possible iron content of kaolin

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pub_title:
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pub_title: Polymorphism of the micas with optical measurements Note: Biotite group
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formula: Au Ag Te4
compound: <missing>
pub_title: The atomic arrangement of sylvanite
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formula: Ba Fe Si4 O10
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formula: Si7 C7
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formula_title: SiC-VI
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formula: Ni Te2
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compound: <missing>
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formula: Ca Al3 (S P) O14 H6
compound: <missing>
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formula_title: <missing>
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formula: K Al3 S2 O14 H6
compound: <missing>
pub_title: Some computations on svanbergite, woodhouseite and alunite
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formula: Si29 C29
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pub_title: Studies on silicon carbide
formula_title: SiC-87R
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formula: K Na3 Si4 Al4 O16
compound: <missing>
pub_title: The structure of nepheline
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formula: Ca2 Al2 Fe Si3 O13 H
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pub_title: The structure of epidote (HCa2(Al,Fe)Al2Si3O13)
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formula: Fe2 Cu S3
compound: <missing>
pub_title: The crystal structure of cubanite
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formula: Na Be Si3 O8 H
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pub_title: The structure of eudidymite (HNaBeSi3O8) Note: this structure does not make any sense
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formula: C4 N2 Br O4
compound: <missing>
pub_title: The structure of diglycine hydrobromide
formula_title: BrN2C4O4
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formula: Na Mg3 Al6 Si6 B3 (O31 H4)
compound: de Kalb, New York, USA
pub_title: The structure of tourmaline
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formula: B5
compound: <missing>
pub_title: The crystal structure of decaborane
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formula: Cu1.4 Te
compound: <missing>
pub_title: Crystal structure of rickardite, Cu4-xTe2
formula_title: <missing>
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b: 3.98
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formula: Cu1.25 Fe.25 S
compound: <missing>
pub_title: On the symmetry and crystal structure of bornite
formula_title: <missing>
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b: 5.47
c: 5.47
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formula: C
compound: <missing>
pub_title: The problem of the graphite structure
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formula: Hg Se
compound: <missing>
pub_title: Description and syntheses of the selenide minerals
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formula: Pb2 Ni3 S2
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pub_title: On parkerite and shandite and the crystal structure of Ni3Pb2S2
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formula: (Au.8 Ag.2) Te2
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pub_title: The atomic arrangement and chemical composition of krennerite
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formula: As2 O3
compound: <missing>
pub_title: The crystal structure of claudetite (monoclinic As2O3)
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formula: Bi V O4
compound: <missing>
pub_title: A preliminary structure for pucherite, BiVO4
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formula: Au Sb2
compound: Giant Yellowknife mine, Northwest Territories, Canada
pub_title: Aurostibite, AuSb2; A new mineral in the pyrite group
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formula: Si19 C19
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pub_title: A new hexagonal polymorph of silicon carbide, 19H
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compound: <missing>
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formula: (Ca1.7 Na.2 K.1) Si2 Mg.5 Al.4 O7
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formula: Ce C O3 F
compound: <missing>
pub_title: The crystallography of bastnaesite, parasite, roentgenite, and synchisite
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formula: Ce2 Ca C O3 F2
compound: <missing>
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pub_title: The crystallography of bastnaesite, parasite, roentgenite, and synchisite
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formula: (Fe.125 V.875) (O2 H)
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formula: Mg1.338 Fe.24 Al.721 Si1.36 O9 H3
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pub_title: Crystal structure of magnesium-vermiculite
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formula: Fe Sb2 S4
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formula: Cu S
compound: Leonard mine, Butte, Montana, USA
pub_title: The crystal structure of covellite, CuS and klockmannite, CuSe
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formula: Cu Se
compound: <missing>
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formula: K Na3 Si4 Al4 O16
compound: <missing>
pub_title: Determination of the crystal structure of nepheline
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formula: U2 Si2 Ca O12
compound: Chinkolobwe deposits, Belgian Congo, Africa
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formula: Fe C O3
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formula: Cu C O3
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formula: Ca Mg C2 O6
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formula: Cd Mg C2 O6
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compound: Synthetic
pub_title: Unit-cell edges of natural and synthetic sphalerites
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formula: Fe As S
compound: <missing>
pub_title: Arsenopyrite crystal-chemical relations From Freiberg, Germany
formula_title: <missing>
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pub_title: The determination and refinement of the structure of narsarsukite, Na2TiOSi4O10
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formula: (K.9 Mn.1) Mg3 (Si3 Fe) O12 H2
compound: <missing>
pub_title: Crystal structure of a trioctahedral mica: Phlogopite
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formula: Zn S
compound: Thomaston Dam, Connecticut
pub_title: Hydrothermal wurtzite at Thomaston Dam, Connecticut
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formula: Ca O2 H2
compound: <missing>
pub_title: A nuclear magnetic resonance determination of the hydrogen positions in Ca(OH)2 T = -190 C
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formula: Ca O2 H2
compound: <missing>
pub_title: A nuclear magnetic resonance determination of the hydrogen positions in Ca(OH)2 T = 25 C
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formula: Pb As2 Fe2 O10 H2
compound: <missing>
pub_title: The crystal structure of carminite
formula_title: <missing>
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formula: Mg5.1 Al1.2 Cr.7 Si3 O18 H8
compound: <missing>
formula_title: <missing>
a: 5.338
b: 9.247
c: 14.435
alpha: 90.0
beta: 97.08
gamma: 90.0
cell_volume: 707.086
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pub_title:
 Chlorite polytypism: II. Crystal structure of a one-layer Cr-chlorite
 Note: variety called kammererite

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formula: Cs (Fe Si2) O6
compound: <missing>
pub_title: A hydrothermally synthesized iron analog of pollucite - Its structure and significance
formula_title: CsFeSi2O6
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formula: Cu1.8 S
compound: <missing>
pub_title: Polymorphism in digenite high-temperature form at T = 80 C
formula_title: <missing>
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formula: Mg3 Si4 O12 N4 C12
compound: <missing>
pub_title: The crystal structure of a hexamethylene-diamine-vermiculite complex
formula_title: <missing>
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b: 9.18
c: 17.12
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formula: Si2 Al2 Ca O12 H8
compound: <missing>
pub_title: The crystal structure determination of the zeolite gismondite. CaAl2Si2O8.4H2O
formula_title: <missing>
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formula: Al2 Be O4
compound: <missing>
pub_title: Refinement of the chrysoberyl structure
formula_title: <missing>
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b: 5.476
c: 4.427
alpha: 90
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formula: (Ta.438 Fe.177 Sn.128 Nb.124 Mn.12 Zr.006 Ti.006 W.001) O2
compound: <missing>
formula_title: <missing>
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b: 4.742
c: 5.152
alpha: 90
beta: 90
gamma: 90
cell_volume: 140.013
crystal_density: 7.375
atoms_sites: ["Ta", "Fe", "Sn", "Nb", "Mn", "Zr", "Ti", "W", "O"]
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pub_title:
 Ixiolite - a columbite substructure
 sample M-6591, note that the coordinates have been put into a standard setting

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formula: Si2 Al2 O9 H4
compound: <missing>
pub_title: Polymorphism of the kaolin minerals
formula_title: <missing>
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pub_title: On the cation and water positions in faujasite
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pub_title: The crystal structure of tunellite, SrB6O9(OH)2.3H2O
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pub_title:
 Studies of the torbernite minerals (I): The crystal structure of abernathyite
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pub_title:
 Studies of the torbernite minerals (I): The crystal structure of abernathyite
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pub_title:
 Studies of the torbernite minerals (I): The crystal structure of abernathyite
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pub_title: Studies of the torbernite minerals (II): The crystal structure of meta-torbernite
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pub_title: The crystal structure of a marialite scapolite
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pub_title:
 The crystal structures of synthetic anhydrous carnotite, K2(UO2)2V2O8, and
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pub_title: Chlorite polytypism: III. Crystal structure of an orthohexagonal iron chlorite
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pub_title:
 The crystal structures of ordered and disordered cobaltite
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formula: Co (As S)
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formula_title: <missing>
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b: 5.582
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pub_title:
 The crystal structures of ordered and disordered cobaltite
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formula: Na B Si3 O8
compound: <missing>
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pub_title:
 Crystal structure of reedmergnerite, a boron albite, and its relation to
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compound: <missing>
pub_title: The crystal structure of laueite, MnFe2(OH)2(PO4)2(H2O)6.2H2O
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compound: <missing>
pub_title: Refinement of the crystal structure of a pyroxene of formula M1M2(Si1.5Al0.5)O6
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formula: Ca (Si4.398 Al1.602) O16.002 H8.004
compound: <missing>
pub_title: The crystal structure of heulandite (Ca,Na2)[Al2Si7O18].6H2O
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formula: Si3.32 Al3.37 Mg2.31 O18 H8
compound: <missing>
pub_title: Structural aspects of dioctahedral chlorite
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formula: Ca Mn Si2 O6
compound: <missing>
pub_title: Refinement of the crystal structure of johannsenite
formula_title: <missing>
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formula: Ca2 Al2 Si3 O12 H2
compound: <missing>
pub_title: Ordering of tetrahedral aluminium in prehnite, Ca2(Al,Fe)[Si3AlO10](OH)2
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formula: Ca Na2 S2 O8
compound: Imperial County, California, USA
pub_title: Refinement of the crystal structure of a glauberite
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formula: (Cs.7 Na.3) (Al.99 Si2.01) O6
compound: <missing>
pub_title: Crystal structure and optical properties of pollucite
formula_title: <missing>
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formula: Mn3 As (O8 H4)
compound: <missing>
formula_title: <missing>
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alpha: 90
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pub_title:
 Crystal chemistry of the basic manganese arsenate minerals 1. The crystal
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formula: Y As Mn2 O8 H4
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formula_title: <missing>
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alpha: 90
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cell_volume: 331.706
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pub_title:
 Crystal chemistry of the basic manganese arsenate minerals 1. The crystal
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formula: Mg3 Si2 O9 H4
compound: <missing>
pub_title: Chlorite polytypism: IV. Regular two-layer structures refined structure
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formula: Ba S O4
compound: <missing>
pub_title: A refinement of the structure of barite from Cow Green mine
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formula: Ca2 Ba Si3 O9
compound: <missing>
pub_title: The crystal structure of walstromite
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formula: K (Si3 Al) O8
compound: St. Gotthard, Switzerland, known as Spencer B, variety adularia
pub_title: The crystal structure of an adularia and a refinement of the structure of orthoclase
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formula: K (Si3 Al) O8
compound: St. Gotthard, Switzerland, known as Spencer C
pub_title: The crystal structure of an adularia and a refinement of the structure of orthoclase
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formula: Ni (As1.23 S.77)
compound: <missing>
pub_title: The crystal structure of disordered gersdorffite
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formula: Sn Ta2 O7
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pub_title:
 Crystal structures and mineral chemistry of double-salt hydrates: II. The
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pub_title: Crystal structure of stilbite
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formula: Cu Fe2 S4 O22 H12
compound: United Verde mine, Jerome, Arizona, USA
pub_title: The crystal structure of ransomite
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formula: Pb2 Cr O5
compound: <missing>
pub_title: A study of phoenicochroite - its structure and properties
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formula: Pb10 Zn Cr6 Si2 O32 F2
compound: <missing>
pub_title: The crystal structure of hemihedrite
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pub_title: Edge-sharing silicate tetrahedra in the crystal structure of leucophoenicite
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pub_title:
 Crystal structures and mineral chemistry of hydrated ferric sulfates. I. The
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pub_title: Refinement of the crystal structures of epidote, allanite and hancockite
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pub_title: Refinement of the crystal structures of epidote, allanite and hancockite
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pub_title: The crystal structure of butlerite
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pub_title: The structure of zircon: A comparison with garnet
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compound: Emerald creek in Latah Co, Idaho, USA
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compound: Asbestos, Quebec, Canada
pub_title: The crystal chemistry of the silicate garnets sample Gr
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pub_title: Cation distribution and atomic thermal vibrations in an iron-rich orthopyroxene
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pub_title: The crystal structure of legrandite
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 Crystal structures of the humite minerals: III. Mg/Fe ordering in humite and its
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 The refinement of the crystal structure of apophyllite II. Determination of the
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 Refinement of the crystal structure of apophyllite III. Determination of the
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pub_title: A novel face-sharing octahedral trimer in the crystal structure of seamanite
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pub_title:
 Crystal chemistry of the basic manganese arsenates: V. Mixed manganese
 coordination in the atomic arrangement of arsenoclasite

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pub_title:
 Crystal structures and mineral chemistry of hydrated ferric sulphates: II. The
 crystal structure of paracoquimbite

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formula: Sr2 B11 O22 H7
compound: old colemanite mine, Lang, Los Angeles County, California, USA
pub_title: Veatchite: Crystal structure and correlations with p-veatchite
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formula: Na.625 Mn1.125 Ca.125 Mg.049 Li.025 Fe1.976 P3 O12
compound: <missing>
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b: 12.533
c: 6.404
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pub_title:
 Crystal chemistry of the alluaudite structure type: Contribution to the
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atoms_sites:
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formula: Ni As2
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formula: (Fe2.34 Mn.63 Mg.03) P2 O8
compound: Bull Moose pegmatite, near Custer, South Dakota, USA
pub_title: Sarcopside: Its atomic arrangement
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formula: (Fe.65 Mn.35) P O4
compound: Fletcher Quarry, North Groton, New Hampshire, USA
pub_title: The crystal structure of heterosite
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b: 9.79
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pub_title: Crystal structures of the high pressure polymorphs of Mn2GeO4
formula_title: Mn2GeO4-beta
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formula: Mn2 Ge O4
compound: <missing>
pub_title: Crystal structures of the high pressure polymorphs of Mn2GeO4
formula_title: Mn2GeO4-delta
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pub_title:
 The crystal structure of talnakhite, Cu18Fe16S32
 model B
 Note: Cu3-U33 changed to match symmetry constraints

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formula: Ca B6 O15 H10
compound: <missing>
pub_title: Gowerite, CaB5O8(OH).B(OH)3.3H2O: Crystal structure and comparison with related borates
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formula: K Fe2 P2 O11 H5
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pub_title: Octahedral tetramer in the crystal structure of leucophosphite, K2[Fe4(OH)2(H2O)2(PO4)4].2H2O
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formula: Cu9.048 S.133 Cl2.001 N.034 O36.699 H33.999
compound: <missing>
pub_title: The disordered, "zeolite-like" structure of connellite
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formula: Si Mg2 O4
compound: hypothetical
formula_title: <missing>
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b: 10.19
c: 5.85
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beta: 90
gamma: 90
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crystal_density: 3.273
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density

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formula: Si Mg2 O4
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 Polymorphs of low and high density

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formula: Si Mg2 O4
compound: hypothetical
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density
 normal

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formula: Si Mg2 O4
compound: hypothetical
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density
 inverse

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formula: Si Mg2 O4
compound: hypothetical
formula_title: Mg2SiO4
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
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 Model I

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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
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 Model II

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formula: Si Mg2 O4
compound: hypothetical
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density
 Model III

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formula: Si Mg2 O4
compound: hypothetical
formula_title: Mg2SiO4
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cell_volume: 121.201
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density
 Sr2PbO4 structure

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formula: Si Mg2 O4
compound: hypothetical
formula_title: Mg2SiO4
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beta: 90
gamma: 90
cell_volume: 128.745
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density
 K2MgF4 structure

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pub_title: The crystal structures of pyrophyllite, 1Tc, and of its dehydroxylate
formula_title: <missing>
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formula_title: <missing>
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pub_title:
 The crystal structures of pyrophyllite, 1Tc, and of its dehydroxylate
 Note: this is polytype pyrophyllite-1Tc

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pub_title: The crystal structure of carletonite, KNa4Ca4Si8O18(CO3)4(F,OH).H2O, a double-sheet silicate
formula_title: <missing>
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