Tetragonal (4*2m) 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.

111p4x2m.gif (2928 bytes)

111      P4i2m 

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

 

112p4x2c.gif (2676 bytes)

112      P4i2c  

(+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)

 

113p4x2i.gif (2374 bytes)

113      P4i21m

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

 

114p4x2i.gif (2293 bytes)

114      P4i21c

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

 

115p4xm2.gif (2801 bytes)

115      P4im2 

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

 

116p4xc2.gif (2600 bytes)

116      P4ic2  

(+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)

 

117p4xb2.gif (2500 bytes)

117      P4ib2  

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

 

118p4xn2.gif (2434 bytes)

118      P4in2  

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

 

119i4xm2.gif (3432 bytes)

119      I4im2

Origins: (0,0,0);  (1/2,1/2,1/2)

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

 

120i4xc2.gif (3215 bytes)

120      I4ic2

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

 

121i4x2m.gif (3554 bytes)

121      I4i2m

Origins: (0,0,0);  (1/2,1/2,1/2)

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

 

122i4x2d.gif (2846 bytes)

122      I4i2d

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

 

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Created 30 March 1999, Last Update 09 May 2008

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