| There are 3 dihedral subgroups: Dih 3, Dih 2, and Dih 1, and 4 cyclic subgroups: Z 6, Z 3, Z 2, and Z 1 | p6, an isogonal hexagon constructed by three mirrors can alternate long |
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| r12 is full symmetry, and a1 is no symmetry |
These symmetries express 9 distinct symmetries of a regular Conway labels these by a letter and group order.