Steven Dutch, Natural and Applied Sciences, University
of Wisconsin  Green Bay
Firsttime Visitors: Please visit Site Map and Disclaimer.
Use "Back" to return here.
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
149 P312
(+x,+y,+z); (y,+xy,+z); (+yx,x,+z);


150 P321
(+x,+y,+z); (y,+xy,+z); (+yx,x,+z);


151 P3_{1} 12
(+x,+y,+z); (y,+xy,1/3+z); (+yx,x,2/3+z);


152 P3_{1} 21
(+x,+y,+z); (y,+xy,1/3+z); (+yx,x,2/3+z);


153 P3_{2} 12
(+x,+y,+z); (y,+xy,2/3+z); (+yx,x,1/3+z);


154 P3_{2} 21
(+x,+y,+z); (y,+xy,2/3+z); (+yx,x,1/3+z);

Rhombohedra are cubes distorted along one of the three fold axes. Coordinates for rhombohedral symmetries can be described in terms of the rhombohedral cell edges or with respect to the threefold symmetry axis system. Coordinates here are given with respect to the threefold symmetry axis system.
155 R32 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);

Return to Symmetry Index
Return to 3dSpace Groups Index
Return to Crustal Materials (MineralogyPetrology) Index
Return to Professor Dutch's Home Page
Created 13 October 1999, Last Update 15 December 2011
Not an official UW Green Bay site