Table 6.

Reduction from 23 to 3

Space group of unstrained crystal, order 12 per lattice point		If stressed so that X = Y; [111] ∥Z				Space group of strained crystal, order 3 per lattice point
		Coordinates referred to axes of unstrained crystal
No.	Symbol	1st Subset	2d Subset	3d Subset	4th Subset	No.	Symbol
195	P23	(x, y, z)	( x, $\overline{y}$, $\overline{z}$)	( $\overline{x}$, y, $\overline{z}$)	( $\overline{x}$, $\overline{y}$, z)	146	R3
		(y, z, x)	( $\overline{y}$, $\overline{z}$, x)	( y, $\overline{z}$, $\overline{x}$)	( $\overline{y}$, z, $\overline{x}$)
		(z, x, y)	( $\overline{z}$, x, $\overline{y}$)	( $\overline{z}$, $\overline{x}$, y)	( z, $\overline{x}$, $\overline{y}$)
196	F23	(x, y, z)	( x, $\overline{y}$, $\overline{z}$)	( $\overline{x}$, y, $\overline{z}$)	( $\overline{x}$, $\overline{y}$, z)	146	R3
		(y, z, x)	( $\overline{y}$, $\overline{z}$, x)	( y, $\overline{z}$, $\overline{x}$)	( $\overline{y}$, z, $\overline{x}$)
		(z, x, y)	( $\overline{z}$, x, $\overline{y}$)	( $\overline{z}$, $\overline{x}$, y)	( z, $\overline{x}$, $\overline{y}$)
197	I23	(x, y, z)	( x, $\overline{y}$, $\overline{z}$)	( $\overline{x}$, y, $\overline{z}$)	( $\overline{x}$, $\overline{y}$, z)	146	R3
		(y, z, x)	( $\overline{y}$, $\overline{z}$, x)	( y, $\overline{z}$, $\overline{x}$)	( $\overline{y}$, z, $\overline{x}$)
		(z, x, y)	( $\overline{z}$, x, $\overline{y}$)	( $\overline{z}$, $\overline{x}$, y)	( z, $\overline{x}$, $\overline{y}$)
198	P213	(x, y, z)	(½+x, ½−y, $\overline{z}$)	( $\overline{x}$, ½+y, ½−z)	(½−x, $\overline{y}$, ½+z)	146	R3
		(y, z, x)	(½−y, $\overline{z}$, ½+x)	(½+y, ½−z, $\overline{x}$)	( $\overline{y}$, ½+z, ½−x)
		(z, x, y)	( $\overline{z}$, ½+x, ½−y)	(½−z, $\overline{x}$, ½+y)	(½+z, ½−x, $\overline{y}$)
199	I213	(x, y, z)	(½+x, ½−y, $\overline{z}$)	( $\overline{x}$, ½+y, ½−z)	(½−x, $\overline{y}$, ½+z)	146	R3
		(y, z, x)	(½−y, $\overline{z}$, ½+x)	(½+y, ½−z, $\overline{x}$)	( $\overline{y}$, ½+z, ½−x)
		(z, x, y)	( $\overline{z}$, ½+x, ½−y)	(½−z, $\overline{x}$, ½+y)	(½+z, ½−x, $\overline{y}$)