Table 13.

Reduction from 422 to 222

Space group of unstrained crystal. order 8 per lattice point		If stressed so that x, y, z ∥ X, Y, Z, any permutation				Space group of strained crystal. order 4 per lattice point
		Coordinates referred to axes of unstrained crystal
No.	Symbol		1st Subset		2d Subset	No.	Symbol
89	P422	(x,y, z) ($\overline{x}$, $\overline{y}$, z)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, y, $\overline{z}$)	(y,x, $\overline{z}$) ($\overline{y}$,$\overline{x}$, $\overline{z}$)	( y, $\overline{x}$, z) ( $\overline{y}$, x, z)	16	P222	21	C222
90	P4212	(x,y, z) ($\overline{x}$$\overline{y}$, z)	(½+x, ½-y,$\overline{z}$) (½-x, ½+y,$\overline{z}$)	(y,x, $\overline{z}$) ($\overline{y}$,$\overline{x}$, $\overline{z}$)	(½+y, ½-x, z) (½-y, ½+x, z)	18	P21212	21	C222
91	P4122	(x,y, z) (x $\overline{y}$, ½+ z)	( x, $\overline{y}$, ½-z) ( $\overline{x}$, y, $\overline{z}$)	(y,x,¾- z) ($\overline{y}$,$\overline{x}$,¼- z)	( y, $\overline{x}$,¾+ z) ( $\overline{y}$, x,¼+ z)	17	P2221	20	C2221
92	P41212	(x,y, z) ($\overline{x}$$\overline{y}$, ½+ z)	(½+x, ½-y, ¾-z) (½-x, ½+y, ¼-z)	(y,x, $\overline{z}$) ($\overline{y}$,$\overline{x}$, ½-z)	(½+y, ½-x, ¾-z) (½-y, ½+x, ¼-z)	19	P212121	20	C2221
93	P4222	(x,y, z) ($\overline{x}$$\overline{y}$, z)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, y, $\overline{z}$)	(y,x,½-z) ($\overline{y}$,$\overline{x}$,½-z)	( y, $\overline{x}$,½+z) ( $\overline{y}$, x,½+z)	16	P222	21	C222
94	P42212	(x,y, z) ($\overline{x}$,$\overline{y}$, z)	(½+x, ½-y, ½-z) (½-x, ½+y, ½-z)	(y,x, $\overline{z}$) ($\overline{y}$,$\overline{x}$, $\overline{z}$)	(½+y, ½-x, ½+z) (½-y, ½+x, ½+z)	18	P21212	21	C222
95	P4322	(x,y, z) ($\overline{x}$$\overline{y}$, ½+ z)	( x, $\overline{y}$, ½-z) ( $\overline{x}$, y, $\overline{z}$)	(y,x,¾- z) ($\overline{y}$,$\overline{x}$,¼- z)	( y, $\overline{x}$,¼+ z) ( $\overline{y}$, x,¾+ z)	17	P2221	20	C2221
96	P43212	(x,y, z) ($\overline{x}$$\overline{y}$, ½+ z)	(½+x, ½-y, ¼-z) (½-x, ½+y, ¾-z)	(y,x, $\overline{z}$) ($\overline{y}$,$\overline{x}$,½-z)	(½+y, ½-x, ¼-z) (½-y, ½+x, ¾-z)	19	P212121	20	C2221
97	1422	(x,y, z) ($\overline{x}$$\overline{y}$, z)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, y, $\overline{z}$)	(y,x, $\overline{z}$) ($\overline{y}$,$\overline{x}$, $\overline{z}$)	( y, $\overline{x}$, z) ( $\overline{y}$, x, z)	23	I222	22	F222
98	14122	(x,y, z) ($\overline{x}$$\overline{y}$, z)	( x, ½-y, ¼-z) ( $\overline{x}$, ½+y, ¼-z)	(y,x, $\overline{z}$) ($\overline{y}$,$\overline{x}$, $\overline{z}$)	( y, ½+x, ¼+z) ( $\overline{y}$, ½+x, ¼+z)	24	I212121	22	F222
No.	Symbol	1st Subset	2d Subset	1st Subset	2d Subset			No.	Symbol
Space group of unstrained crystal, order 8 per lattice point		Coordinates referred to axes of unstrained crystal						Space group of strained crystal, order 4 per lattice point
		If stressed so that [1$\overline{1}$0], [110], z ∥ X, Y, Z, any permutation