# Tetragonal (422) 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.

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 89   P422) (+x,+y,+z); (-x,-y,+z); (-x,+y,-z); (+x,-y,-z) (+y,-x,+z); (-y,+x,+z); ( +y,+x,-z); (-y,-x,-z) 90   P4212) (+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) 91   P4122) (+x,+y,+z); (-x,-y,1/2+z -y,+x,1/4+z); (+y,-x,3/4+z) (-x,+y,-z); (+x,-y,1/2-z -y,-x,1/4-z); (+y,+x,3/4-z); () 92   P41212) (+x,+y,+z); (-x,-y, 1/2+z); (1/2-y, 1/2+x, 1/4+z); (1/2+y, 1/2-x,3/4+z);  (+y,+x,-z); (-y,-x, 1/2-z); (1/2-x, 1/2+y, 1/4-z); (1/2+x, 1/2-y, 3/4-z) 93   P42 22) (+x,+y,+z); (-x,-y,+z); (+y,-x, 1/2+z); (-y,+x, 1/2+z) (-x,+y,-z); (+x,-y,-z); (+y,+x, 1/2-z); (-y,-x, 1/2-z) 94   P42 212) (+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) 95   P43 22) (+x,+y,+z); (-x,-y,1/2+z); (+y,-x,1/4+z); (-y,+x,3/4+z ) (-x,+y,-z); (+x,-y,1/2-z); (+y,+x,1/4-z); (-y,-x,3/4-z) 96   P43 212) (+x,+y,+z); (-x,-y,1/2+z);  (1/2+y, 1/2-x,1/4+z); (1/2-y, 1/2+x, 3/4+z); (-x,+y,-z); (+x,-y,1/2-z); (1/2+y, 1/2+x,1/4-z); (1/2-y, 1/2-x,3/4-z) 97   I422 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) 98   I4122 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)

(Created 30 March 1999, Last Update 15 December 2011

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