Rotation Subgroups
Given in IUC notation, Coxeter notation, (orbifold notation), the rotational/translational subgroups are:
| Reflection | Mixed | Improper rotation/trans-reflection | Rotation/translation | Commutator subgroup |
|---|---|---|---|---|
| pmm, (*2222) | pm, (**) | cm, (*×) pg, (××) pgg, (22×) |
p1, (o) | p2, +, (2222) |
| cmm, (2*22) pmg, (22*) |
p2, +, (2222) | |||
| p4m, (*442) | p4g, (4*2) | p4, +, (442) | ||
| p3m1, ], (*333) | p3, ]+, (333) | p3, ]+, (333) | ||
| p6m, (*632) | p31m, (3*3) | p6, +, (632) | ||
Read more about this topic: List Of Planar Symmetry Groups
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“The lazy manage to keep up with the earth’s rotation just as well as the industrious.”
—Mason Cooley (b. 1927)