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 (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, International Tables for Crystallography, vol. E (5th ed.), Berlin, New York: Springer-Verlag, doi:10.1107/97809553602060000105, ISBN 978-1-4020-0715-6