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.

089-p422.gif (2706 bytes)

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)

090p42i2.gif (2308 bytes)

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)

091p4i22.gif (2437 bytes)

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); ()

092p4i2i.gif (2194 bytes)

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)

093p4j22.gif (2545 bytes)

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)

094p4j2i.gif (2324 bytes)

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)

095p4k22.gif (2430 bytes)

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)

096p4k2i.gif (2173 bytes)

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)

097-i422.gif (3076 bytes)

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)

098i4i22.gif (3164 bytes)

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)

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(Created 30 March 1999, Last Update 31 May 2020