Tetragonal (4/m) Space Groups

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, University of 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.

083-p4_m.gif (1855 bytes)

83        p4/m

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

 
084p4j_m.gif (1841 bytes)

84        p42/m

(+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)

 
085-p4_n.gif (1797 bytes)

85        p4/n

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

 
086p4j_n.gif (1812 bytes)

86        p42/n

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

 
087-i4_m.gif (2208 bytes)

87        i4/m           

Origins: (0,0,0    1/2.1/2,1/2)

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

 
088i4i_a.gif (2254 bytes)

88        i41/a           

Origins: (0,0,0    1/2.1/2,1/2)

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

 

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Created 30 March 1999, Last Update 31 May 2020