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:

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

Among these groups, there are 8 enantiomorphic pairs.

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

• 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

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