Trigonal (3 and 3*) Space Groups
Steven Dutch, Natural and Applied Sciences, University
of Wisconsin - Green Bay
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.
3-fold and 6-fold coordinates are tabulated with respect to axes intersecting at 60 degrees. In this oblique coordinate system, coordinates tend to be simple
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143 P3 (+x,+y,+z); (-y,+x-y,+z); (+y-x,-x,+z |
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144 P31 (+x,+y,+z); (-y,+x-y,1/3+z); (+y-x,-x,2/3+z |
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145 P32 (+x,+y,+z); (-y,+x-y,2/3+z); (+y-x,-x,1/3+z |
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146 R3 Origins: (0,0,0); (1/3,2/3,2/3); (2/3,1/3,1/3) (+x,+y,+z); (-y,+x-y,+z); (+y-x,-x,+z |
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147 P3i (+x,+y,+z); (-y,+x-y,+z); (+y-x,-x,+z |
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148 R3i Origins: (0,0,0); (1/3,2/3,2/3); (2/3,1/3,1/3) (+x,+y,+z); (-y,+x-y,+z); (+y-x,-x,+z |
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Created 13 October 1999, Last Update 15 December 2011
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