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:
Triclinic1 p12 p Monoclinic/inclined3 p2114 pm115 pc116 p2/m117 p2/c11 Monoclinic/orthogonal8 p1129 p112110 p11m11 p112/m12 p1121/m Orthorhombic13 p22214 p222115 pmm216 pcc217 pmc2118 p2mm19 p2cm20 pmmm21 pccm22 pmcm Tetragonal23 p424 p4125 p4226 p4327 p28 p4/m29 p42/m30 p42231 p412232 p422233 p432234 p4mm35 p42cm, p42mc36 p4cc37 p2m, pm238 p2c, pc239 p4/mmm40 p4/mcc41 p42/mmc, p42/mcm Trigonal42 p343 p3144 p3245 p46 p312, p32147 p3112, p312148 p3212, p322149 p3m1, p31m50 p3c1, p31c51 pm1, p1m52 pc1, p1c Hexagonal53 p654 p6155 p6256 p6357 p6458 p6559 p60 p6/m61 p63/m62 p62263 p612264 p622265 p632266 p642267 p652268 p6mm69 p6cc70 p63mc, p63cm71 pm2, p2m72 pc2, p2c73 p6/mmm74 p6/mcc75 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
External links "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