Arithmetic crystal class

Back to the page arithmetic crystal classes

Three-dimensional arithmetic crystal classes.

Crystal systems	Crystal class
	Geometric	Arithmetic
		Number	Symbol
Triclinic	$1$	1	$1P$
	${\bar 1}$	2	${\bar 1}P$
Monoclinic	$2$	3	$2P$
	$m$	4	$2C$
		5	$mP$
	$2/m$	6	$mC$
		7	$2/m P$
		8	$2/mC$
Orthorhombic	$222$	9	$222P$
		10	$222C$
		11	$222F$
		12	$222I$
	$mm$	13	$mm2P$
		14	$mm2C$
		15	$2mmC$
			$(mm2A)$
		16	$mm2F$
		17	$mm2I$
	$mmm$	18	$mmmP$
		19	$mmmC$
		20	$mmmF$
		21	$mmmI$
Tetragonal	$4$	22	$4P$
		23	$4I$
	${\bar 4}$	24	${\bar 4}P$
		25	${\bar 4}I$
	$4/m$	26	$4/mP$
		27	$4/mI$
	$422$	28	$422P$
		29	$422I$
	$4mm$	30	$4mmP$
		31	$4mmI$
	${\bar 4}m$	32	${\bar 4}2mP$
		33	${\bar 4}m2P$
		34	${\bar 4}m2I$
		35	${\bar 4}2mI$
	$4/mmm$	36	$4/mmmP$
		37	$4/mmmI$
Trigonal	$3$	38	$3P$
		39	$3R$
	${\bar 3}$	40	${\bar 3}P$
		41	${\bar 3}R$
	$32$	42	$312P$
		43	$321P$
		44	$32R$
	$3m$	45	$3m1P$
		46	$31mP$
		47	$3mR$
	${\bar 3}m$	48	${\bar 3}1mP$
		49	${\bar 3}m1P$
		50	${\bar 3}mR$
Hexagonal	$6$	51	$6P$
	${\bar 6}$	52	${\bar 6}P$
	$6/m$	53	$6/mP$
	$622$	54	$622P$
	$6mm$	55	$6mmP$
	${\bar 6}m$	56	${\bar 6}2mP$
		57	${\bar 6}m2P$
	$6/mmm$	58	$6/mmm$
Cubic	$23$	59	$23P$
		60	$23F$
		61	$23I$
	$m{\bar 3}$	62	$m{\bar 3}P$
		63	$m{\bar 3}F$
		64	$m{\bar 3}I$
	$432$	65	$432P$
		66	$432F$
		67	$432I$
	${\bar 4}3m$	68	${\bar 4}3m P$
		69	${\bar 4}3m F$
		70	${\bar 4}3m I$
	$m{\bar 3}m$	71	$m{\bar 3}mP$
		72	$m{\bar 3}mF$
		73	$m{\bar 3}mI$