A regular dodecahedron (a twelve-sided gaming die

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Group theory and symmetry · Group theory and symmetry

Invariance, Ch Groups: the algebra of symmetry operations

Problem

A regular dodecahedron (a twelve-sided gaming die, each face a regular pentagon) has a rotation group of order 60, as for the icosahedron and for

\mathrm{C_{60}}

. Its 12 faces form a single orbit under this rotation group. Using the orbit-stabiliser theorem, find the order of the subgroup of rotations that fixes one face (that is, the rotations about the axis through that face's centre and the centre of the opposite face).

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