Tetragonal (4/m) Space Groups

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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.

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 15 December 2011

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