p6majo, 16/2/2017

This book collects a set of worksheets that are used to illustrate properties of polytopes, which are representations of geometric groups, so called coxeter groups. The action of these groups amounts to symmetry transformations (rotations and reflections) acting on polytopes (polyhedra in three dimensions).

The most general polyhedron that is a representation of H3 is the great rhombicosidodecahedron. Its number of vertices coincides with the number of group elements of H3. Since H3 is transitive, you can generate the full rhombicosidodecahedron by applying all group elements acting on one single starting point. All other representations can be obtained by moving alike faces inward. These transformations are shown in the three worksheets of this chapter.

• 1. Great rhombicosidodecahedron to soccer ball
• 2. Conversion to Rhombicosidodecahedron
• 3. Great rhombicosidodecahedron to soccer ball