2013

Shaping Space

Exploring Polyhedra in Nature, Art, and the Geometrical Imagination

Editors:

ISBN: 978-0-387-92713-8 (Print) 978-0-387-92714-5 (Online)

Table of contents (22 chapters)

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  1. Front Matter

    Pages i-x

  2. First Steps

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-11

      Introduction to the Polyhedron Kingdom

    3. No Access

      Book Chapter

      Pages 13-40

      Six Recipes for Making Polyhedra

    4. No Access

      Book Chapter

      Pages 41-52

      Regular and Semiregular Polyhedra

    5. No Access

      Book Chapter

      Pages 53-63

      Milestones in the History of Polyhedra

    6. No Access

      Book Chapter

      Pages 65-75

      Polyhedra: Surfaces or Solids?

    7. No Access

      Book Chapter

      Pages 77-86

      Dürer’s Problem

  3. Polyhedra in Nature and Art

    1. Front Matter

      Pages 87-87

    2. No Access

      Book Chapter

      Pages 89-107

      Exploring the Polyhedron Kingdom

    3. No Access

      Book Chapter

      Pages 109-123

      Spatial Perception and Creativity

    4. No Access

      Book Chapter

      Pages 125-138

      Goldberg Polyhedra

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      Book Chapter

      Pages 139-151

      Polyhedra and Crystal Structures

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      Book Chapter

      Pages 153-170

      Polyhedral Molecular Geometries

    7. No Access

      Book Chapter

      Pages 171-189

      Form, Function, and Functioning

  4. Polyhedra in the Geometrical Imagination

    1. Front Matter

      Pages 191-191

    2. No Access

      Book Chapter

      Pages 193-199

      The Polyhedron Kingdom Tomorrow

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      Book Chapter

      Pages 201-209

      Paneled and Molecular Polyhedra: How Stable Are They?

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      Book Chapter

      Pages 211-216

      Duality of Polyhedra

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      Book Chapter

      Pages 217-222

      Combinatorial Prototiles

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      Book Chapter

      Pages 223-229

      Polyhedra Analogues of the Platonic Solids

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      Book Chapter

      Pages 231-251

      Convex Polyhedra, Dirichlet Tessellations, and Spider Webs

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      Book Chapter

      Pages 253-255

      Uniform Polyhedra from Diophantine Equations

    9. No Access

      Book Chapter

      Pages 257-266

      Torus Decompostions of Regular Polytopes in 4-space

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