Polyhedra - Department of Mathematics

Contents
1. Introduction 2
1.1. Basic Terms for Describing Polyhedra 2
2. Polyhedra 3
2.1. What is a Polyhedron? 3
2.2. Convex Polyhedra 3
2.2.1. The Platonic Polyhedra 3
2.2. Duality of Polyhedra 4
3. Inclusions of Polyhedra 6
3.1. Nested Platonic Solids 8
4. Compounds of Polyhedra 10
4.1. Forming Compound by Observing Duality 10
4.2. Forming Compound by Observing Inclusions 10
4.3. Forming Compound by Observing Symmetry 11
4.4. Transitivity 13
5. Stellations of Polyhedra 16
5.1. Edge-stellations 16
5.2. Face-stellations 16
5.3. Stellations of the Dodecahedron 17
6. Deltahedra 19
6.1. Pyramids 19
6.2. Convex Deltahedra 19
6.2.1. Classification 19
6.3.2. Geometric Realization 23
6.2.3. What About Other Polygons? 26
7. Zonohedra 27
7.1. Rhombic Polyhedra 27
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