Tetragonal (4mm); 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.

099-p4mm.gif (2694 bytes);

99      p4mm

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

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

100-p4bm.gif (2265 bytes);

100      p4bm

(+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);

101p4jcm.gif (2552 bytes);

101     p42cm

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

102p4jnm.gif (2341 bytes);

102     p42nm

(+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);

103-p4cc.gif (2453 bytes);

103     p4cc

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

104-p4nc.gif (2114 bytes);

104     p4nc

(+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)

105p4jmc.gif (2515 bytes);

105     p42mc

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

106p4jbc.gif (2105 bytes);

106     p42bc

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

107-i4mm.gif (3000 bytes);

107     i4mm

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)

108-i4cm.gif (2843 bytes);

108     i4cm

Origins: (0, 0, 0 (1/2.1/2, 1/2);

(+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)

109i4imd.gif (2730 bytes);

109     i41md

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

110i4icd.gif (2482 bytes);

110     i41cd

Origins: (0, 0, 0);  (1/2.1/2, 1/2);

(+x, +y, +z); (-x, -y, 1/2+z);
(+y, 1/2+x, 3/4+z); (-y, 1/2-x, 3/4+z)
(-x, +y, +z); (+x, -y, 1/2+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 11 June 2020