Rod group

In mathematics, a rod group is a three-dimensional line group whose point group is one of the axial crystallographic point groups. This constraint means that the point group must be the symmetry of some three-dimensional lattice.

Table of the 75 rod groups, organized by crystal system or lattice type, and by their point groups:

Triclinic
1	p1	2	p1
Monoclinic/inclined
3	p211	4	pm11	5	pc11	6	p2/m11	7	p2/c11
Monoclinic/orthogonal
8	p112	9	p1121	10	p11m	11	p112/m	12	p1121/m
Orthorhombic
13	p222	14	p2221	15	pmm2	16	pcc2	17	pmc21
18	p2mm	19	p2cm	20	pmmm	21	pccm	22	pmcm
Tetragonal
23	p4	24	p41	25	p42	26	p43	27	p4
28	p4/m	29	p42/m	30	p422	31	p4122	32	p4222
33	p4322	34	p4mm	35	p42cm, p42mc	36	p4cc	37	p42m, p4m2
38	p42c, p4c2	39	p4/mmm	40	p4/mcc	41	p42/mmc, p42/mcm
Trigonal
42	p3	43	p31	44	p32	45	p3	46	p312, p321
47	p3112, p3121	48	p3212, p3221	49	p3m1, p31m	50	p3c1, p31c	51	p3m1, p31m
52	p3c1, p31c
Hexagonal
53	p6	54	p61	55	p62	56	p63	57	p64
58	p65	59	p6	60	p6/m	61	p63/m	62	p622
63	p6122	64	p6222	65	p6322	66	p6422	67	p6522
68	p6mm	69	p6cc	70	p63mc, p63cm	71	p6m2, p62m	72	p6c2, p62c
73	p6/mmm	74	p6/mcc	75	p6/mmc, p6/mcm

The double entries are for orientation variants of a group relative to the perpendicular-directions lattice.

Among these groups, there are 8 enantiomorphic pairs.

See also

• Point group
• Crystallographic point group
• Space group
• Line group
• Frieze group
• Layer group

References

• Hitzer, E.S.M.; Ichikawa, D. (2008), "Representation of crystallographic subperiodic groups by geometric algebra" (PDF), Electronic Proc. of AGACSE (3, 17–19 Aug. 2008), Leipzig, Germany, archived from the original (PDF) on 2012-03-14
• Kopsky, V.; Litvin, D.B., eds. (2002), International Tables for Crystallography, Volume E: Subperiodic groups, vol. E (5th ed.), Berlin, New York: Springer-Verlag, doi:10.1107/97809553602060000105, ISBN 978-1-4020-0715-6

External links

• Bilbao Crystallographic Server, under "Subperiodic Groups: Layer, Rod and Frieze Groups"
• Nomenclature, Symbols and Classification of the Subperiodic Groups, V. Kopsky and D. B. Litvin