© 2013

Shaping Space

Exploring Polyhedra in Nature, Art, and the Geometrical Imagination

  • Marjorie Senechal


  • Makes the geometric world of polyhedra accessible to professionals, students, and laypeople

  • Dedicated to the memory of the legendary geometer H. S. M. Coxeter and the many-faceted design scientist Arthur L. Loeb

  • Not to be missed book for schools, public libraries, and coffee table sections of bookstores

  • Many contributions by outstanding authors make this book intriguing


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

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

About the editors

Marjorie Senechal, a world leader in mathematical crystallography, is Louise Wolff Kahn Professor Emerita in Mathematics and History of Science and Technology at Smith College, where she taught from 1966 to 2007. In 2007, she received the College's Honored Professor Award.

Professor Senechal is currently Senior Fellow of the Kahn Liberal Arts Institute at Smith and editor-in-chief of The Mathematical Intelligencer, a cultural journal for the international community of mathematical scientists. Her areas of mathematics research are discrete geometry, tiling theory, and mathematical crystallography. In addition to numerous articles, she is the author or editor of ten books, including Quasicrystals and Geometry, Long Life to Your Children! (a portrait of High Albania), and American Silk, 1830 - 1930, entrepreneurs and artifacts.

Bibliographic information


From the reviews:

“It consists of a collection of essays by different authors about many different aspects related to polyhedra. … The book is amply illustrated and aiming at a public from 9 till 99. It will be of interest to a very broad public. Form a mathematical side children might be interested in geometrical puzzles and advanced mathematicians may be interested in solving the open problems, and the whole range in between will probably find something interesting of their own taste.” (A. Bultheel, The European Mathematical Society, June, 2013)