Table 22.

Reduction from 222 to 2

Space group of unstrained crystal, order 4 per lattice point		If stressed so that x ∥ X, Y, or Z		Space group of strained crystal, order 2 per lattice point		If stressed so that y ∥ X, Y, or Z		Space group of strained crystal, order 2 per lattice point		If stressed so that z ∥ X, Y, or Z		Space group of strained crystal, order 2 per lattice point
		Coordinates referred to axes of unstrained crystal				Coordinates referred to axes of unstrained crystal				Coordinates referred to axes of unstrained crystal
No.	Symbol	1st Subset	2d Subset	No.	Symbol	1st Subset	2d Subset	No.	Symbol	1st Subset	2d Subset	No.	Symbol
16	P222	( x, y, z) ( x, $\overline{y}$, $\overline{z}$)	( $\overline{x}$, y, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, z)	3	P2	( x, y, z) ( $\overline{x}$, y, $\overline{z}$)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, z)	3	P2	( x,y, z) ( $\overline{x}$,$\overline{y}$, z)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, y, $\overline{z}$)	3	P2
17	P2221	( x, y, z) ( x, $\overline{y}$, $\overline{z}$)	( $\overline{x}$, y, ½- z) ( $\overline{x}$, $\overline{y}$, ½+ z)	3	P2	( x, y, z) ( $\overline{x}$, y, ½- z)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, ½+ z)	3	P2	( x,y, z) ( $\overline{x}$,$\overline{y}$, ½+ z)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, y, ½- z)	4	P21
18	P21212	( x, y, z) (½+x, ½-y, $\overline{z}$)	(½-x, ½+ y, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, z)	4	P21	( x, y, z) (½-x, ½+y, $\overline{z}$)	(½+x, ½- y, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, z)	4	P21	( x,y, z) ( $\overline{x}$,$\overline{y}$, z)	(½+x, ½- y, $\overline{z}$) (½-x, ½+ y, $\overline{z}$)	3	P2
19	P212121	( x, y, z) (½+x, ½-y, $\overline{z}$)	( $\overline{x}$, ½+ y, ½- z) (½-x, $\overline{y}$, ½+ z)	4	P21	( x, y, z) ( $\overline{x}$, ½+y , ½- z)	(½+x, ½- y, $\overline{z}$) (½-x, $\overline{y}$, ½+ z)	4	P21	( x,y, z) (½-x,$\overline{y}$, ½+z)	(½+x, ½- y, $\overline{z}$) ( $\overline{x}$,½+y, ½- z)	4	P21
20	C2221	( x, y, z) ( x, $\overline{y}$, $\overline{z}$)	( $\overline{x}$, y, ½- z) ( $\overline{x}$, $\overline{y}$, ½+ z)	5	C2	( x, y, z) ( $\overline{x}$, y, ½- z)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, ½+ z)	5	C2	( x,y, z) ( $\overline{x}$,$\overline{y}$, ½+ z)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, y, ½- z)	4	P21
21	C222	( x, y, z) ( x, $\overline{y}$, $\overline{z}$)	( $\overline{x}$, y, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, z)	5	C2	( x, y, z) ( $\overline{x}$, y, $\overline{z}$)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, z)	5	C2	( x,y, z) ( $\overline{x}$,$\overline{y}$, z)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, y, $\overline{z}$)	3	P2
22	F222	( x, y, z) ( x, $\overline{y}$, $\overline{z}$)	( $\overline{x}$, y, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, z)	5	C2	( x, y, z) ( $\overline{x}$, y, $\overline{z}$)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, z)	5	C2	( x,y, z) ( $\overline{x}$,$\overline{y}$, z)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, y, $\overline{z}$)	5	C2
23	I222	( x, y, z) ( x, $\overline{y}$, $\overline{z}$)	( $\overline{x}$, y, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, z)	5	C2	( x, y, z) ( $\overline{x}$, y, $\overline{z}$)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, $\overline{y}$, z)	5	C2	( x,y, z) ( $\overline{x}$,$\overline{y}$, z)	( x, $\overline{y}$, $\overline{z}$) ( $\overline{x}$, y, $\overline{z}$)	5	C2
24	I212121	( x, y, z) (½+x, ½-y, $\overline{z}$)	( $\overline{x}$, ½+ y, ½- z) (½-x, $\overline{y}$, ½+ z)	5	C2	( x, y, z) ( $\overline{x}$, ½+y , ½+ z)	(½+x, ½- y, $\overline{z}$) (½-x, $\overline{y}$, ½+ z)	5	C2	( x,y, z) (½-x,$\overline{y}$, ½+z)	(½+x, ½- y, $\overline{z}$) ( $\overline{x}$,½+y, ½- z)	5	C2