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.
139); I4/mmm Origins: (0,0,0); (1/2,1/2,1/2) (+x,+y,+z); (x,y,+z); (x,+y,+z); (+x,y,+z) 

140); I4/mcm Origins: (0,0,0); (1/2,1/2,1/2) (+x,+y,+z); (x,y,+z); (x,+y, 1/2+z); (+x,y,1/2+z) 

141); I41/amd Origins: (0,0,0); (1/2,1/2,1/2) (+x,+y,+z); (x,y,+z); 

142); I41/acd Origins: (0,0,0); (1/2,1/2,1/2) (+x,+y,+z); (+x,y,1/2+z); 
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Created 13 October 1999, Last Update 15 December 2011
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