Shaping Space

Exploring Polyhedra in Nature, Art, and the Geometrical Imagination

  • Marjorie Senechal

Table of contents

  1. Front Matter
    Pages i-x
  2. First Steps

    1. Front Matter
      Pages 1-1
    2. Marjorie Senechal
      Pages 3-11
    3. Marion Walter, Jean Pedersen, Magnus Wenninger, Doris Schattschneider, Arthur L. Loeb, Erik Demaine et al.
      Pages 13-40
    4. H. S. M. Coxeter
      Pages 41-52
    5. Joseph Malkevitch
      Pages 53-63
    6. Arthur L. Loeb
      Pages 65-75
    7. Joseph O’Rourke
      Pages 77-86
  3. Polyhedra in Nature and Art

    1. Front Matter
      Pages 87-87
    2. Marjorie Senechal
      Pages 89-107
    3. Janos Baracs
      Pages 109-123
    4. George Hart
      Pages 125-138
    5. Chung Chieh
      Pages 139-151
    6. Magdolna Hargittai, Istvan Hargittai
      Pages 153-170
    7. George Fleck
      Pages 171-189
  4. Polyhedra in the Geometrical Imagination

    1. Front Matter
      Pages 191-191
    2. Marjorie Senechal
      Pages 193-199
    3. Branko Grünbaum, G. C. Shephard
      Pages 211-216
    4. Egon Schulte
      Pages 217-222
    5. Jörg M. Wills
      Pages 223-229
    6. Walter Whiteley, Peter F. Ash, Ethan Bolker, Henry Crapo
      Pages 231-251
    7. Thomas F. Banchoff
      Pages 257-266
    8. Robert Connelly
      Pages 267-278
    9. Moritz W. Schmitt, Günter M. Ziegler
      Pages 279-289
  5. Back Matter
    Pages 291-341

About this book


Molecules, galaxies, art galleries, sculptures, viruses, crystals, architecture, and more: Shaping Space—Exploring Polyhedra in Nature, Art, and the Geometrical Imagination is an exuberant survey of polyhedra and at the same time a hands-on, mind-boggling introduction to one of the oldest and most fascinating branches of mathematics.

Some of the world’s leading geometers present a treasury of ideas, history, and culture to make the beauty of polyhedra accessible to students, teachers, polyhedra hobbyists, and professionals such as architects and designers, painters and sculptors, biologists and chemists, crystallographers, physicists and earth scientists, engineers and model builders, mathematicians and computer scientists.

The creative chapters by more than 25 authors explore almost every imaginable side of polyhedra.  From the beauty of natural forms to the monumental constructions made by man, there is something to fascinate every reader. The book is dedicated to the memory of the legendary geometer H. S. M. Coxeter and the multifaceted design scientist Arthur L. Loeb.

Contributing Authors: P. Ash, T. F. Banchoff, J. Baracs, E. Bolker, C. Chieh, R. Connelly, H.S.M. Coxeter, H. Crapo, E. Demaine, M. Demaine, G. Fleck, B. Grünbaum, I. Hargittai, M. Hargittai, G. Hart, V. Hart, A. Loeb, J. Malkevitch, B. Monson, J. O'Rourke, J. Pedersen, D. Schattschneider, M. Schmitt, E. Schulte, M. Senechal, G.C. Shephard, I. Streinu, M. Walter, M. Wenninger, W. Whiteley, J. M. Wills, and G. M. Ziegler.


Dirichlet tessellations Torus decompositions combinatorial prototiles crystal structures geometrical imagination interdisciplinary molecular geometries platonic solids polyhedral three-dimensional shape

Editors and affiliations

  • Marjorie Senechal
    • 1
  1. 1.Dept. Mathematics & StatisticsSmith CollegeNorthamptonUSA

Bibliographic information