Symmetries of a regular dodecagon, with markups Reworked from "The Symmetries of Things", Chapter 20 The regular dodecagon has Dih12 dihedral symmetry, order 24, and 15 lower dihedral and cyclic symmetries. The dihedral symmetries pass through vertices (d) and edges (p), or both (i). Cyclic symmetries in the middle column are labeled as g for their central gyration orders.