Table 3.
Reduction from 432 to 422
Space group of unstrained crystal, order 24 per lattice point | If stressed so that X=Y; z∥Z | Space group of strained crystal, order 8 per lattice point | ||||
---|---|---|---|---|---|---|
Coordinates referred to axes of unstrained crysta | ||||||
No. | Symbol | 1st Subset | 2d Subset | 3d Subset | No. | Symbol |
207 | P432 | ( x, y, z) ( y, x, ) | ( y, z, x) ( z, y, ) | ( z, x, y) ( x, z, ) | 89 | P422 |
( , x, z) ( , y, ) | ( , y, x) ( , z, ) | ( , z, y) ( y, x, z) | ||||
( , , z) ( , , ) | ( , , x) ( , , ) | ( , , y) ( , , ) | ||||
( y, , z) ( x, , ) | ( z, , x) ( y, , ) | ( x, , y) ( z, , ) | ||||
208 | P4232 | ( x, y, z) (½+y,½+x,½−z) | ( y, z, x) (½+z,½+y,½−x) | ( z, x, y) (½+x,½+z,½−y) | 93 | P4222 |
(½−y,½+x,½+z) ( , y, ) | (½−z,½+y,½+x) ( . z, ) | (½−x,½+z,½+y) ( , x, ) | ||||
( , , z) (½−y,½−x,½−z) | ( , , x) (½−z,½−y,½−x) | ( , , y) (½−x,½−z,½−y) | ||||
(½+y,½−x,½+z) ( x, , ) | (½+z,½−y,½+x) ( y, , ) | (½+x,½−z,½+y) ( z, , ) | ||||
209 | F432 | ( x, y, z) ( y, x, ) | ( y, z, x) ( z, y, ) | ( z, x, y) ( x, z, ) | 97 | I422 |
( , x, z) ( , y, ) | ( , y, x) ( , z, ) | ( , z, y) ( , x, ) | ||||
( , , z) ( , , ) | ( , , x) ( , , ) | ( , , y) ( , , ) | ||||
( y, , z) ( x, , ) | ( z, , x) ( y, , ) | ( x, , y) ( z, , ) | ||||
210 | F4132 | ( x, y, z) (¼+y,¼+x,¼−z) | ( y, z, x) (¼+z,¼+y,¼−x) | ( z, x, y) (¼+x,¼+z,¼−y) | 98 | I4122 |
(¼−y,¼+x,¼+z) ( , y, ) | (¼−z,¼+y,¼+x) ( , z, ) | (¼−x,¼+z,¼+y) ( , x, y) | ||||
( , , z) (¼−y,¼−x,¼−z) | ( , , x) (¼−z,¼−y,¼−x) | ( , , y) (¼+x,¼−z,¼−y) | ||||
(¼+y,¼−x,¼+z) ( x, , ) | (¼+z,¼−y,¼+x) ( y, , ) | (¼+x,¼−z,¼+y) ( z, , ) | ||||
211 | I432 | ( x, y, z) ( y, x, ) | ( y, z, x) ( z, y, ) | ( z, x, y) ( x, z, ) | 97 | I422 |
( , x, z) ( , y, ) | ( , y, x) ( y, x, z) | ( , z, y) ( , x, ) | ||||
( , , z) ( , , ) | ( , , x) ( , , x) | ( , , y) ( , , ) | ||||
( y, , z) ( x, , ) | ( z, , x) ( y, , ) | ( x, , y) ( z, , ) | ||||
212 | P4332 | ( x, y, z) (¼+y,¾+x,¾−z) | ( y, z, x) (¼+z,¾+y,¾−x) | ( z, x, y) (¼+x,¾+z,¾−y) | 96 | P43212 |
(¾−y,¼+x,¾+z) ( ,½+y,½−z) | (¾−z,¼+y,¾+x) ( ,½+z,½−x) | (¾−x,¼+z,¾+y) ( ,½+x,½−y) | ||||
(½−x, ,½+z) (¼−y,¼−x,¼−z) | (½−y, ,½+x) (¼−z,¼−y,¼−x) | (½−z, ,½+y) (¼−x,¼−z,¼−y) | ||||
(¾+y,¾−x,¼+z) (½+x,½−y, ) | (¾+z,¾−y,¼+x) (½+y,½−z, ) | (¾+x,¾−z,¼+y) (½+z,½−x, ) | ||||
213 | P4132 | ( x, y, z) (¾+y,¾+x,¼−z) | ( y, z, x) (¾+z,¼+y,¼−x) | ( z, x, y) (¾+x,¼+ z,¼−y) | 92 | P41212 |
(¼−y,¾+x,¼+z) ( ,½+y,½−z) | (¼−z,¾+y,¼+x) ( ,½+z,½−x) | (¼−x,¾+z,¼+y) ( ,½+x,½−y) | ||||
(½−x, ,½+z) (¾−y,¾−x,¾−z) | (½−y, ,½+x) (¾−z,¾−y,¾−x) | (½−z, ,½+y) (¾−x,¾−z,¾−y) | ||||
(¼+y,¼−x,¾+z) (½+x,½−y, ) | (¼+z,¼−y,¾+x) (½+y,½−z, ) | (¼+x,¼−z,¾+y) (½+z,½−x, ) | ||||
214 | I4132 | ( x, y, z) (¼+y,¾+x,¾−z) | ( y, z, x) (¼+z,¾+y,¾−x) | ( z, x, y) (¼+x,¾+z,¾−y) | 98 | I4122 |
(¾−y,¼+x,¾+z) ( ,½+y,½−z) | (¾−z,¼+y,¾+x) ( ,½+z,½−x) | (¾−x,¼+z,¾+y) ( ,½+x,½−y) | ||||
(½−x, ,½+z) (¼−y,¼−x,¼−z) | (½−y, ,½+x) (¼−z,¼−y,¼−x) | (½−z, ,½+y) (¼−x,¼−z,¼−y) | ||||
(¾+y,¾−x,¼+z) (½+x,½−y, ) | (¾+z,¾−y,¼+x) (½+y,½−z, ) | (¾+x,¾−z,¼+y) (½+z,½−x, ) |