Tetragonal (4 and 4*) 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.

075-p4.gif (1517 bytes)

75 p4

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


076-p4i.gif (1429 bytes)

76 p41

(+x,+y,+z); (-x,-y,1/2+z); (+y,-x,3/4+z);  (-y,+x,1/4+z)


077-p4j.gif (1462 bytes)

77 p42

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


078-p4k.gif (1399 bytes)

78 p43

(+x,+y,+z); (-x,-y,1/2+z); (+y,-x,1/4+z); (-y,+x,3/4+z)


079-i4.gif (1778 bytes)

79  i4    

Origins: (0,0,0    1/2.1/2,1/2)

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


080-i4i.gif (1594 bytes)

80  i41  

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)


081-p4x.gif (1474 bytes)

81 p4*

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


082-i4x.gif (1768 bytes)

82  i4*  

Origins: (0,0,0    1/2.1/2,1/2)

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


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Created 30 March 1999, Last Update 31 May 2020