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.
3fold and 6fold coordinates are tabulated with respect to axes intersecting at 60 degrees. In this oblique coordinate system, coordinates tend to be simple
156 P3m1
(+x,+y,+z); (y,+xy,+z); (+yx,x,+z);


157 P31m
(+x,+y,+z); (y,+xy,+z); (+yx,x,+z);


158 P3c1
(+x,+y,+z); (y,+xy,+z); (+yx,x,+z);


159 P31m
(+x,+y,+z); (y,+xy,+z); (+yx,x,+z);

160 R3m Origins (0,0,0); (1/3, 2/3, 2/3); (2/3, 1/3, 1/3); (+x, +y, +z); (y, +xy, +z); (+yx, x, +z); 

161 R3c Origins (0,0,0); (1/3, 2/3, 2/3); (2/3, 1/3, 1/3); (+x, +y, +z); (y, +xy, +z); (+yx, x, +z); 
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Created 13 October 1999, Last Update 15 December 2011
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