Orthorhombic (222) Space Groups

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.

016-p222.gif (1834 bytes) 16. P222

(x,y,z); (-x,-y,z); (x,-y,-z); (-x,y,-z)

017p222i.gif (1977 bytes) 17. P2221

(x,y,z); (x,-y,-z); (-x,-y,1/2+z); (-x,y,1/2-z)

018p2i2i2.gif (1617 bytes) 18. P21212

(x,y,z); (-x,-y,z); (1/2+x,1/2-y,z); (1/2-1/2+y,-z)

019-p2ii.gif (1632 bytes) 19. p212121

(x,y,z); (1/2-x,-y,1/2+z); (1/2+x,1/2-y,-z); (-x,1/2+1/2-z)

020-c22i.gif (2146 bytes) 20. C2221

(x,y,z); (x,-y,-z); (-x,-y,1/2+z); (-x,y,1/2-z);
Origins: (0,0,0); (1/2,1/2,0)

021-c222.gif (2015 bytes) 21. C222

(x,y,z); (-x,-y,z); (x,-y,-z); (-x,y,-z);
Origins: (0,0,0); (1/2,1/2,0)

022-f222.gif (2620 bytes) 22. F222

(x,y,z); (-x,-y,z); (x,-y,-z); (-x,y,-z);
Origins: (0,0,0); (0,1/2,1/2); (1/2,0,1/2); (1/2,1/2,0)

023-i222.gif (2022 bytes)  

23. I222

(x,y,z); (-x,-y,z); (x,-y,-z); (-x,y,-z);
Origins: (0,0,0); (1/2,1/2,1/2)

024-i2ii.gif (2050 bytes) 24. I212121

(x,y,z); (1/2-x,-y,1/2+z); (1/2+x,1/2-y,z); (-x,1/2+y,1/2-z);
Origins: (0,0,0); (1/2,1/2,1/2)

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Created 30 March 1999, Last Update 20 December 1999