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
168 P6 (+x, +y, +z); (y, +xy, +z);
(+yx, x, +z); 

169 P6_{1} (+x, +y, +z); (y, +xy, 1/3+z);
(+yx, x, 2/3+z); 

170 P6_{5} (+x, +y, +z); (y, +xy, 2/3+z);
(+yx, x, 1/3+z); 

171 P6_{2} (+x, +y, +z); (y, +xy, 2/3+z);
(+yx, x, 1/3+z); 

172 P6_{4} (+x, +y, +z); (y, +xy, 1/3+z);
(+yx, x, 2/3+z); 

173 P6_{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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