# Orthorhombic (2/m 2/m 2/m) Space Groups (C, F and I Lattices)

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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To the right of each space group is a listing of coordinate points. These are the coordinates to which a general point (x,y,z) is transformed by the space group. Origins (called "equivalent points" in the International Tables), are additional points around which the points are transformed. For example, (0,0,0) refers to a corner of the unit cell, (1/2,1/2,1/2) to the center. All space groups have origin (0,0,0). For a space group with an additional origin (1/2,1/2,1/2), point (x,y,z) is also transformed to (1/2+x,1/2+y,1/2+z) and so on.

## C Lattices

 63        Cmcm            Origins: (0,0,0   1/2,1/2,0) (+x,+y,+z); (-x,-y, 1/2+z); (+x,-y,-z); (-x,+y, 1/2-z) (-x,-y,-z); (+x,+y, 1/2-z); ( -x,+y,+z); ( +x,-y, 1/2+z) 64        Cmca             Origins: (0,0,0   1/2,1/2,0)         (+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) 65        Cmmm            Origins: (0,0,0   1/2,1/2,0)         (+x,+y,+z); (-x,-y,+z); (+x,-y,-z); (-x,+y,-z) (-x,-y,-z); (+x,+y,-z); (-x,+y,+z); ( +x,-y,+z) 66        Cccm            Origins: (0,0,0   1/2,1/2,0) (+x,+y,+z); (-x,-y,+z); (-x,-y,-z); (+x,+y,-z) (+x,-y,1/2-z); (-x,+y,1/2-z); (-x,+y,1/2+z); (+x,-y,1/2+z) 67        Cmma              Origins: (0,0,0   1/2,1/2,0) (+x,+y,+z); (-x,+y,-z); (1/2-x,+y,+z); (1/2+x,+y,-z) (-x,-y,-z); (+x,-y,+z); (1/2+x,-y,-z); (1/2-x,-y,+z) 68        Ccca            Origins: (0,0,0   1/2,1/2,0) (+x,+y,+z); (-x,-y,+z); (+x,-y,-z); (-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)

## F Lattices

 69        Fmmm             Origins: (0,0,0    0,1/2,1/2    1/2,0,1/2   1/2,1/2,0)         (+x,+y,+z); (-x,-y,+z); (+x,-y,-z); (-x,+y,-z) (-x,-y,-z); (+x,+y,-z); (-x,+y,+z); ( +x,-y,+z) 70        Fddd            Origins: (0,0,0    0,1/2,1/2    1/2,0,1/2   1/2,1/2,0) (+x,+y,+z); (-x,-y,+z); (+x,-y,-z); (-x,+y,-z) (1/4-x,1/4-y,1/4-z); (1/4+x,1/4+y,1/4-z); (1/4-x,1/4+y,1/4+z); (1/4+x,1/4-y,1/4+z)

## I Lattices

 71        Immm            Origins: (0,0,0    1/2.1/2,1/2)      (+x,+y,+z); (-x,-y,+z); (+x,-y,-z); (-x,+y,-z) (-x,-y,-z); (+x,+y,-z); (-x,+y,+z); ( +x,-y,+z) 72        Ibam                Origins: (0,0,0    1/2.1/2,1/2) (+x,+y,+z); (-x, -y,+z); (+x, -y, 1/2-z); (-x, +y, 1/2-z) (-x,-y,-z); (+x, +y,-z); ( -x, +y, 1/2+z); (+x, -y, 1/2+z) 73        Ibca            Origins: (0,0,0    1/2.1/2,1/2) (+x,+y,+z); (-x, 1/2-y,+z); (+x, -y, 1/2-z); (1/2-x, +y,-z) (-x,-y,-z); (+x, 1/2+y,-z); (-x, +y, 1/2+z); (1/2+x, -y,+z) 74        Imma                Origins: (0,0,0    1/2.1/2,1/2) (+x,+y,+z); (-x, 1/2+y,-z); (-x,+y,+z); ( +x, 1/2+y,-z) (-x,-y,-z); (+x, 1/2-y,+z); (+x,-y,-z); (-x, 1/2-y,+z)