Tetragonal (4/m 2/m 2/m) Space Groups

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.

139i4_mm.gif (4858 bytes)

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)
(+x,+y,-z); (-x,-y,-z); (-x,+y,-z); (+x,-y,-z)
(+y,+x,+z); (-y,-x,+z); (-y,+x,+z); (+y,-x,+z)
(+y,+x,-z); (-y,-x,-z); (-y,+x,-z); (+y,-x,-z)

140i4_mc.gif (3837 bytes)

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)
(+x,+y,-z); (-x,-y,-z); (-x,+y, 1/2-z); (+x,-y, 1/2-z)
(-y,+x,+z); (+y,-x,+z); (+y,+x, 1/2+z); (-y,-x, 1/2+z)
(-y,+x,-z); (+y,-x,-z); (+y,+x, 1/2-z); (-y,-x, 1/2-z)

141i4i_a.gif (5325 bytes)

141); I41/amd

Origins: (0,0,0); (1/2,1/2,1/2)

(+x,+y,+z); (-x,-y,+z);
(+x, 1/2+y,1/4-z); (-x, 1/2-y, 1/4-z)
(-x,+y,+z); (+x,-y,+z);
(-x, 1/2+y,1/4-z); ( ); (+x, 1/2-y, 1/4-z)
(+y,+x,-z); (-y,-x,-z);
(+y, 1/2+x,1/4+z); (-y, 1/2-x, 1/4+z)
(-y,+x,-z); (+y,-x,-z);
(-y, 1/2+x,1/4+z); (+y, 1/2-x, 1/4+z)

142i4i_a.gif (5371 bytes)

142); I41/acd

Origins: (0,0,0); (1/2,1/2,1/2)

(+x,+y,+z); (+x,-y,1/2+z);
(+x, 1/2+y,1/4-z); (+x, 1/2-y, 3/4-z)
(-x,-y,+z); (-x,+y,1/2+z);
(-x, 1/2-y,1/4-z); ( ); (-x, 1/2+y, 3/4-z)
(-y,+x,-z); (+y,+x,1/2-z);
(-y, 1/2+x,1/4+z); (+y, 1/2+x, 3/4+z)
(+y,-x,-z); (-y,-x,1/2-z);
(+y, 1/2-x,1/4+z); (-y, 1/2-x, 3/4+z)

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Created 13 October 1999, Last Update 15 December 2011

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