Unformatted text preview: Chapter 4 Symmetries of Polyhedra 4.1. Rotations of Regular Polyhedra There are five regular polyhedra: the tetrahedron, the cube, the octahe- dron, the dodecahedron (12 faces), and the icosahedron (20 faces). See Figure 4.1.1 on the following page . In this section, we will work out the rotational symmetry groups of the tetrahedron, cube, and octahedron, and in the following section we will treat the dodecahedron and icosahedron. In later sections, we will work out the full symmetry groups, with reflections allowed as well as rotations. It is convenient to have physical models of the regular polyhedra that you can handle while studying their properties. In case you can’t get any ready-made models, I have provided you (at the end of the book, Appendix E) with patterns for making paper model. I urge you to obtain or construct models of the regular polyhedra before continuing with your reading....
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- Fall '08
- Algebra, Polyhedron, Rotational symmetry, Point groups in three dimensions, regular polyhedra