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  • © 2013

Shaping Space

Exploring Polyhedra in Nature, Art, and the Geometrical Imagination

  • 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
  • Includes supplementary material: sn.pub/extras

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-x
  2. First Steps

    1. Front Matter

      Pages 1-1
    2. Introduction to the Polyhedron Kingdom

      • Marjorie Senechal
      Pages 3-11
    3. Six Recipes for Making Polyhedra

      • Marion Walter, Jean Pedersen, Magnus Wenninger, Doris Schattschneider, Arthur L. Loeb, Erik Demaine et al.
      Pages 13-40
    4. Regular and Semiregular Polyhedra

      • H. S. M. Coxeter
      Pages 41-52
    5. Milestones in the History of Polyhedra

      • Joseph Malkevitch
      Pages 53-63
    6. Polyhedra: Surfaces or Solids?

      • Arthur L. Loeb
      Pages 65-75
    7. Dürer’s Problem

      • Joseph O’Rourke
      Pages 77-86
  3. Polyhedra in Nature and Art

    1. Front Matter

      Pages 87-87
    2. Exploring the Polyhedron Kingdom

      • Marjorie Senechal
      Pages 89-107
    3. Spatial Perception and Creativity

      • Janos Baracs
      Pages 109-123
    4. Goldberg Polyhedra

      • George Hart
      Pages 125-138
    5. Polyhedra and Crystal Structures

      • Chung Chieh
      Pages 139-151
    6. Polyhedral Molecular Geometries

      • Magdolna Hargittai, Istvan Hargittai
      Pages 153-170
    7. Form, Function, and Functioning

      • George Fleck
      Pages 171-189
  4. Polyhedra in the Geometrical Imagination

    1. Front Matter

      Pages 191-191
    2. The Polyhedron Kingdom Tomorrow

      • Marjorie Senechal
      Pages 193-199
    3. Duality of Polyhedra

      • Branko GrĂĽnbaum, G. C. Shephard
      Pages 211-216
    4. Combinatorial Prototiles

      • 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.

Reviews

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)

Editors and Affiliations

  • Dept. Mathematics & Statistics, Smith College, Northampton, USA

    Marjorie Senechal

About the editor

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

  • Book Title: Shaping Space

  • Book Subtitle: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination

  • Editors: Marjorie Senechal

  • DOI: https://doi.org/10.1007/978-0-387-92714-5

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Marjorie Senechal 2013

  • Hardcover ISBN: 978-0-387-92713-8Published: 22 March 2013

  • Softcover ISBN: 978-1-4939-3948-0Published: 23 August 2016

  • eBook ISBN: 978-0-387-92714-5Published: 22 March 2013

  • Edition Number: 1

  • Number of Pages: X, 341

  • Topics: Geometry, Crystallography and Scattering Methods, Design, general

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 69.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access