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 p63/mmc, p63/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

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