Table 10.

Reduction from $\overline{4}2m$ to mm2

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}$2m	[1$\overline{1}$0], [110],z ∥ X, Y, Z, any permutation.	(x, y, z)	( y, x, z)	( x, $\overline{y}$, $\overline{z}$)	(y, $\overline{x}$, $\overline{z}$)	35	Cmm2
			($\overline{x}$, $\overline{y}$, z)	($\overline{y}$, $\overline{x}$, z)	( $\overline{x}$, y, $\overline{z}$)	($\overline{y}$, x, $\overline{z}$)
112	P$\overline{4}$2c	Do.	(x, y, z)	( y, x,½+ z)	( x, $\overline{y}$,½-z)	(y, $\overline{x}$, $\overline{z}$)	37	Ccc2
			($\overline{x}$, $\overline{y}$, z)	($\overline{y}$, $\overline{x}$,½+z)	( $\overline{x}$, y,½-z)	($\overline{y}$, x, $\overline{z}$)
113	P$\overline{4}$21m	Do,	(x, y, z)	(½+y,½+x, z)	(½+x,½-y, $\overline{z}$)	(y, $\overline{x}$, $\overline{z}$)	35	Cmm2
			($\overline{x}$, $\overline{y}$, z)	(½-y,½-x, z)	(½-x,½+y, $\overline{z}$)	($\overline{y}$, x, $\overline{z}$)
114	P$\overline{4}$21c	Do,	(x, y, z)	(½+y,½+x,½+ z)	(½+x,½-y,½-z)	(y, $\overline{x}$, $\overline{z}$)	37	Ccc2
			($\overline{x}$, $\overline{y}$, z)	(½-y,½-x,½+z)	(½-x,½+y,½-z)	($\overline{y}$, x, $\overline{z}$)
115	P$\overline{4}$m2	x, y, z ∥. X, Y, Z, any permutation.	(x, y, z)	( x, $\overline{y}$, z)	( y, x, $\overline{z}$)	(y, $\overline{x}$, $\overline{z}$)	25	Pmm2
			($\overline{x}$, $\overline{y}$, z)	( $\overline{x}$, y, z)	($\overline{y}$, $\overline{x}$, $\overline{z}$)	($\overline{y}$, x, $\overline{z}$)
116	P$\overline{4}$c2	Do.	(x, y, z)	( x, $\overline{y}$,½+z)	( y, x,½-z)	(y, $\overline{x}$, $\overline{z}$)	27	Pcc2
			($\overline{x}$, $\overline{y}$, z)	( $\overline{x}$, y,½+z)	($\overline{y}$, $\overline{x}$,½-z)	($\overline{y}$, x, $\overline{z}$)
117	P4b2	Do.	(x, y, z)	(½+x,½-y, z)	(½+y,½+x, $\overline{z}$)	(y, $\overline{x}$, $\overline{z}$)	32	Pba2
			($\overline{x}$, $\overline{y}$, z)	(½-x,½-y, z)	(½-y,½-x, $\overline{z}$)	($\overline{y}$, x, $\overline{z}$)
118	P$\overline{4}$n2	Do.	(x, y, z)	(½+x,½-y,½+z)	(½+y,½+x,½-z)	(y, $\overline{x}$, $\overline{z}$)	34	Pnn2
			($\overline{x}$, $\overline{y}$, z)	(½-x,½+y,½+z)	(½-y,½-x,½-z)	($\overline{y}$, x, $\overline{z}$)
119	I$\overline{4}$m2	Do.	(x, y, z)	( x, $\overline{y}$, z)	( y, x, $\overline{z}$)	(y, $\overline{x}$, $\overline{z}$)	44	Imm2
			($\overline{x}$, $\overline{y}$, z)	( $\overline{x}$, y, z)	($\overline{y}$, $\overline{x}$, $\overline{z}$)	($\overline{y}$, x, $\overline{z}$)
120	I$\overline{4}$c2	Do.	(x, y, z)	( x, $\overline{y}$,½+z)	( y, x,½-z)	(y, $\overline{x}$, $\overline{z}$)	45	Iba2
			($\overline{x}$, $\overline{y}$, z)	( $\overline{x}$, y,½+z)	($\overline{y}$, $\overline{x}$,½-z)	($\overline{y}$, x, $\overline{z}$)
121	I$\overline{4}$2m	[1$\overline{1}$0]. [110], z ∥ X, Y, Z, any permutation.	(x, y, z)	( y, x, z)	( x, $\overline{y}$, $\overline{z}$)	(y, $\overline{x}$, $\overline{z}$)	42	Fmm2
			($\overline{x}$, $\overline{y}$, z)	($\overline{y}$, $\overline{x}$, z)	( $\overline{x}$, y, $\overline{z}$)	($\overline{y}$, x, $\overline{z}$)
122	I$\overline{4}$2d	Do.	(x, y, z)	( y,½+x,¼+ z)	( x,½-y,¼-z)	(y, $\overline{x}$, $\overline{z}$)	43	Fdd2
			($\overline{x}$, $\overline{y}$, z)	( $\overline{y}$,½-x,¼+ z)	( $\overline{x}$,½+y,¼-$\overline{z}$)	($\overline{y}$, x, $\overline{z}$)