Table 9.

Reduction from 622 to 222

Space group of unstrained crystal, order 12 per lattice point		If stressed so that y and z ∥ any two of X, Y, and Z			Space group of strained crystal, order 4 per lattice point
		Coordinates referred to axes of unstrained crysta
No.	Symbol	1st Subset	2d Subset	3d Subset	No.	Symbol
177	P622	(x, y, z)	($\overline{y}$,x-y, z)	(y-x,$\overline{x}$, z)	21	C222
		(x,x-y, $\overline{z}$)	($\overline{y}$, $\overline{x}$, $\overline{z}$)	(y-x,y, $\overline{z}$)
		($\overline{x}$, $\overline{y}$, z)	(y, y -x, z)	(x-y,x, z)
		($\overline{x}$, y-x, $\overline{z}$)	(y, x, $\overline{z}$)	(x- y, $\overline{y}$, $\overline{z}$)
178	P6122	(x, y, z)	($\overline{y}$,x-y,⅓+z)	(y-x,$\overline{x}$,⅔+z)	20	C2221
		(x,x-y,⅙-z)	($\overline{y}$, $\overline{x}$,⅚-z)	(y-x,y,½-z)
		($\overline{x}$, $\overline{y}$,½+z)	(y, y -x,⅚+z)	(x-y,x,⅙+z))
		($\overline{x}$, y-x,⅔-z)	(y x,⅓-z)	(x- y, $\overline{y}$, $\overline{z}$)
179	P6522	(x, y, z)	($\overline{y}$,x-y,⅔+z)	(y-x,$\overline{x}$,⅓+z)	20	C2221
		(x,x-y,⅚-z)	($\overline{y}$, $\overline{x}$,⅙-z)	(y-x,y,½-z)
		($\overline{x}$, $\overline{y}$,½+z)	(y, y -x,⅙+z)	(x-y,x,⅚+z)
		($\overline{x}$, y-x,⅓-z)	(y x,⅔-z)	(x- y, $\overline{y}$, $\overline{z}$)
180	P6222	(x, y, z)	($\overline{y}$,x-y,⅔+z)	(y-x,$\overline{x}$,⅓+z)	21	C222
		(x,x-y,⅓-z)	($\overline{y}$, $\overline{x}$,⅔-z)	(y-x,y, $\overline{z}$)
		($\overline{x}$, $\overline{y}$, z)	(y, y -x,⅔+z)	(x-y,x,⅓+z)
		($\overline{x}$, y-x,⅓-z)	(y x,⅔-z)	(x- y, $\overline{y}$, $\overline{z}$)
181	P6422	(x, y, z)	($\overline{y}$,x-y,⅓+z)	(y-x,$\overline{x}$,⅔+z)	21	C222
		(x,x-y,⅔-z)	($\overline{y}$, $\overline{x}$,⅓-z)	(y-x,y, $\overline{z}$)
		($\overline{x}$, $\overline{y}$, z)	(y, y -x,⅓+z)	(x-y,x,⅔+z)
		($\overline{x}$, y-x,⅔-z)	(y x,⅓-z)	(x- y, $\overline{y}$, $\overline{z}$)
182	P6322	(x, y, z)	($\overline{y}$,x-y, z)	(y-x,$\overline{x}$, z)	20	C2221
		(x,x-y,½-z)	($\overline{y}$, $\overline{x}$,½-z)	(y-x,y,½-z)
		($\overline{x}$, $\overline{y}$,½+z)	(y, y -x,½+z)	(x-y,x,½+z)
		($\overline{x}$, y-x, $\overline{z}$)	(y, x, $\overline{z}$)	(x- y, $\overline{y}$, $\overline{z}$)