Rod group

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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.

Contents

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

Triclinic
1p12p1
Monoclinic/inclined
3p2114pm115pc116p2/m117p2/c11
Monoclinic/orthogonal
8p1129p112110p11m11p112/m12p1121/m
Orthorhombic
13p22214p222115pmm216pcc217pmc21
18p2mm19p2cm20pmmm21pccm22pmcm
Tetragonal
23p424p4125p4226p4327p4
28p4/m29p42/m30p42231p412232p4222
33p432234p4mm35p42cm, p42mc36p4cc37p42m, p4m2
38p42c, p4c239p4/mmm40p4/mcc41p42/mmc, p42/mcm
Trigonal
42p343p3144p3245p346p312, p321
47p3112, p312148p3212, p322149p3m1, p31m50p3c1, p31c51p3m1, p31m
52p3c1, p31c
Hexagonal
53p654p6155p6256p6357p64
58p6559p660p6/m61p63/m62p622
63p612264p622265p632266p642267p6522
68p6mm69p6cc70p63mc, p63cm71p6m2, p62m72p6c2, p62c
73p6/mmm74p6/mcc75p63/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