Unformatted text preview: W n 2 Z g , consists of one, two, or three vertices. 4.1.8. Show that we have accounted for all of the rotational symmetries of the cube. 4.2. Rotations of the Dodecahedron and Icosahe-dron The dodecahedron and icosahedron are dual to each other and so have the same rotational symmetry group. We need only work out the rotation group of the dodecahedron. See Figure 4.2.1 . Figure 4.2.1. Dodecahedron and icosahedron. The dodecahedron has six 5–fold axes through the centroids of oppo-site faces, giving 24 rotations of order 5. See Figure 4.2.2 on the facing page ....
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- Fall '08
- Algebra, Polyhedron, Rotational symmetry, Dodecahedron, rotational symmetries