# Tetragonal (422) Space Groups

(Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof Wisconsin - Green Bay

To the right of each space group is a listing of coordinate points. These are thecoordinates to which a general point (x,y,z) is transformed by the space group. Origins(called "equivalent points" in the International Tables), areadditional points around which the points are transformed. For example, (0,0,0) refers toa 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 alsotransformed 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 31 May 2020

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