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.
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131 p42/mcm (+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); (-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);
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132 p42/mmc (+x, +y,
+z); (-x, -y, +z); (-x, +y, 1/2+z); (+x, -y, 1/2+z); (+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); (+y, +x, -z); (-y, -x,
-z); (-y, +x, 1/2-z); (+y, -x, 1/2-z);
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133 p42/nbc (+x, +y,
+z); (-x, +y, 1/2-z); (1/2-x, 1/2+y, +z); (1/2+x, 1/2+y, 1/2-z);
(-x, -y, +z); (+x, -y, 1/2-z); (1/2+x, 1/2-y, +z); (1/2-x, 1/2-y,
1/2-z); (-y, +x, -z); (+y, +x, 1/2+z); (1/2+y, 1/2+x, -z); (1/2-y,
1/2+x, 1/2+z); (+y, -x, -z); (-y, -x, 1/2+z); (1/2-y, 1/2-x,
-z); (1/2+y, 1/2-x, 1/2+z);
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134 p42/nnm (+x, +y,
+z); (-x, -y, +z); (1/2+x, 1/2+y, 1/2-z); (1/2-x, 1/2-y, 1/2-z);
(-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); (+y, +x, +z); (-y, -x, +z); (1/2+y, 1/2+x, 1/2-z);
(1/2-y, 1/2-x, 1/2-z);
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135 p42/mbc (+x, +y,
+z); (-y, +x, 1/2+z); (1/2+x, 1/2-y, +z); (1/2+y, 1/2+x, 1/2+z);
(+x, +y, -z); (-y, +x, 1/2-z); (1/2+x, 1/2-y, -z); (1/2+y, 1/2+x,
1/2-z); (-x, -y, +z); (+y, -x, 1/2+z); (1/2-x, 1/2+y, +z); (1/2-y,
1/2-x, 1/2+z); (-x, -y, -z); (+y, -x, 1/2-z); (1/2-x, 1/2+y,
-z); (1/2-y, 1/2-x, 1/2-z);
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136 p42/mnm (+x, +y,
+z); (-x, -y, +z); (1/2+x, 1/2+y, 1/2-z); (1/2-x, 1/2-y, 1/2-z);
(-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);
(+y, +x, -z); (-y, -x, -z); (1/2+y, 1/2+x, 1/2+z); (1/2-y, 1/2-x, 1/2+z);
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137 p42/nmc (+x, +y,
+z); (-x, -y, +z); (1/2+x, 1/2+y, 1/2-z); (1/2-x, 1/2-y, 1/2-z);
(-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); (+y, +x, -z); (-y, -x, -z); (1/2+y, 1/2+x, 1/2+z);
(1/2-y, 1/2-x, 1/2+z);
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138 p42/ncm (+x, +y,
+z); (-x, +y, 1/2+z); (1/2-x, 1/2+y, -z); (1/2+x, 1/2+y, 1/2-z);
(-x, -y, +z); (+x, -y, 1/2+z); (1/2+x, 1/2-y, -z); (1/2-x, 1/2-y,
1/2-z); (-y, +x, -z); (+y, +x, 1/2-z); (1/2+y, 1/2+x, +z); (1/2-y,
1/2+x, 1/2+z); (+y, -x, -z); (-y, -x, 1/2-z); (1/2-y, 1/2-x,
+z); (1/2+y, 1/2-x, 1/2+z);
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