Table 11.

Reduction from $\overline{4}2m$ to 222

Space group of unstrained crystal, order 8 per lattice point		If stressed so that	Coordinates referred to axes of unstrained crystal				Space group of strained crystal, order 4 per lattice point
No.	Symbol		1st Subset		2d Subset		No.	Symbol
111	P$\overline{4}$2m	x, y, z II X, Y, Z, any permutation.	(x, y, z)	( x, $\overline{y}$, $\overline{z}$)	( y, x, z)	(y, $\overline{x}$, $\overline{z}$)	16	P222
			($\overline{x}$, $\overline{y}$, z)	($\overline{x}$, y, $\overline{z}$)	( $\overline{y}$, $\overline{x}$, z)	($\overline{y}$, x, $\overline{z}$)
112	P$\overline{4}$2c	Do.	(x, y, z)	( x, $\overline{y}$,½-z)	( y, x,½+z)	(y, $\overline{x}$, $\overline{z}$)	16	P222
			($\overline{x}$, $\overline{y}$, z)	($\overline{x}$, y,½-z)	( $\overline{y}$, $\overline{x}$,½+z)	($\overline{y}$, x, $\overline{z}$)
113	P$\overline{4}$21m	Do.	(x, y, z)	(½+x,½-y, $\overline{z}$)	(½+y,½+x, z)	(y, $\overline{x}$, $\overline{z}$)	18	P21212
			($\overline{x}$, $\overline{y}$, z)	(½-x,½+y, $\overline{z}$)	(½-y,½-x, z)	($\overline{y}$, x, $\overline{z}$)
114	P$\overline{4}$21C	Do.	(x, y, z)	(½+x,½-y,½-z)	(½+y,½+x,½+z)	(y, $\overline{x}$, $\overline{z}$)	18	P21212
			($\overline{x}$, $\overline{y}$, z)	(½-x,½+y,½-z)	(½-y,½-x,½+z)	($\overline{y}$, x, $\overline{z}$)
115	P$\overline{4}$m2	[1$\overline{1}$0], [110], z ∥ X, Y, Z, any permutation.	(x, y, z)	( y, x, $\overline{z}$)	( x, $\overline{y}$, z)	(y, $\overline{x}$, $\overline{z}$)	21	C222
			($\overline{x}$, $\overline{y}$, z)	( $\overline{y}$, $\overline{x}$, $\overline{z}$)	($\overline{x}$, y, z)	($\overline{y}$, x, $\overline{z}$)
116	P$\overline{4}$c2	Do.	(x, y, z)	( y, x,½-z)	( x, $\overline{y}$,½+z)	(y, $\overline{x}$, $\overline{z}$)	21	C222
			($\overline{x}$, $\overline{y}$, z)	( $\overline{y}$, $\overline{x}$,½-z)	($\overline{x}$, y,½+z)	($\overline{y}$, x, $\overline{z}$)
117	P$\overline{4}$b2	Do.	(x, y, z)	( ½+y,½+x, $\overline{z}$)	(½+x,½-y, z)	(y, $\overline{x}$, $\overline{z}$)	21	C222
			($\overline{x}$, $\overline{y}$, z)	( ½-y,½-x, $\overline{z}$)	(½-x,½-y, z)	($\overline{y}$, x, $\overline{z}$)
118	P$\overline{4}$n2	Do.	(x, y, z)	( ½+y,½+x,½-z)	(½+x,½-y,½+z)	(y, $\overline{x}$, $\overline{z}$)	21	C222
			($\overline{x}$, $\overline{y}$, z)	( ½-y,½-x,½-z)	(½-x,½+y,½+z)	($\overline{y}$, x, $\overline{z}$)
119	1$\overline{4}$m2	Do.	(x, y, z)	( y, x, $\overline{z}$)	( x, $\overline{y}$, z)	(y, $\overline{x}$, $\overline{z}$)	22	F222
			($\overline{x}$, $\overline{y}$, z)	( $\overline{y}$, $\overline{x}$, $\overline{z}$)	($\overline{x}$, y, z)	($\overline{y}$, x, $\overline{z}$)
120	1$\overline{4}$c2	Do.	(x, y, z)	( y, x,½-z)	( x, $\overline{y}$,½+z)	(y, $\overline{x}$, $\overline{z}$)	22	F222
			($\overline{x}$, $\overline{y}$, z)	( $\overline{y}$, $\overline{x}$,½-z)	($\overline{x}$, y,½+z)	($\overline{y}$, x, $\overline{z}$)
121	I$\overline{4}$2m	x, y, z ∥ X, Y, Z, any permutation.	(x, y, z)	( x, $\overline{y}$, $\overline{z}$)	( y, x, z)	(y, $\overline{x}$, $\overline{z}$)	23	I222
			($\overline{x}$, $\overline{y}$, z)	($\overline{x}$, y, $\overline{z}$)	( $\overline{y}$, $\overline{x}$, z)	($\overline{y}$, x, $\overline{z}$)
122	I$\overline{4}$2d	Do.	(x, y, z)	( x,½-y,¼-z)	( y,½+x,¼+z)	(y, $\overline{x}$, $\overline{z}$)	24	I212121
			($\overline{x}$, $\overline{y}$, z)	($\overline{x}$,½-y,¼-z)	($\overline{y}$,½-x,¼+z)	($\overline{y}$, x, $\overline{z}$)