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

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof Wisconsin - Green Bay

To the right of each space group is a listing of coordinate points. These are thecoordinates to which a general point (x,y,z) is transformed by the space group. Origins(called "equivalent points" in the International Tables), areadditional points around which the points are transformed. For example, (0,0,0) refers toa 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 alsotransformed to (1/2+x,1/2+y,1/2+z) and so on.

C Lattices

063-cmcm.gif (2753 bytes)

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)

 
064-cmca.gif (2976 bytes)

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)

 
065-cmmm.gif (2953 bytes)

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)

 
066-cccm.gif (2744 bytes)

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)

 
067-cmma.gif (2970 bytes)

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)

 
068-ccca.gif (3016 bytes)

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

069-fmmm.gif (3392 bytes)

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)

 
070-fddd.gif (4199 bytes)

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

071-immm.gif (2901 bytes)

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)

 
072-ibam.gif (2733 bytes)

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)

 
073-ibca.gif (2938 bytes)

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)

 
074-imma.gif (3030 bytes)

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)

 

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Created 30 March 1999, Last Update 31 May 2020