Shaping Space : Exploring Polyhedra in Nature Art and the Geometrical Imagination 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. ORourke 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. Preface I First Steps. 1 Introduction to the Polyhedron Kingdom. Marjorie Senechal 2 Six Recipes for Making Polyhedra. Marion Walter; Jean Pedersen; MagnusWenninger; Doris Schattschneider; Arthur Loeb; and Eric Demaine Martin Demaine and Vi Hart 3 Regular and Semiregular Polyhedra. H. S. M. Coxeter 4 Milestones in the History of Polyhedra. Joseph Malkevitch 5 Polyhedra: Surfaces or Solids Arthur Loeb 6 Dürers Problem. Joseph ORourke II Polyhedra in Nature and Art 7 Exploring the Polyhedron Kingdom. Marjorie Senechal 8 Spatial Perception and Creativity. Janos Baracs 9 Goldberg Polyhedra. George Hart 10 Polyhedra and Crystal Structures. Chung Chieh 11 Polyhedral Molecular Geometries. Magdolna Hargittai and Istvan Hargittai 12 Form Function and Functioning. George Fleck III Polyhedra in the Geometrical Imagination 13 The Polyhedron Kingdom Tomorrow. Marjorie Senechal 14 Paneled and Molecular Polyhedra: How Stable Are They Ileana Streinu 15 Duality of Polyhedra. Banko Grünbaum and G. C. Shephard 16 Combinatorial Prototiles. Egon Schulte 17 Polyhedra Analogues of the Platonic Solids. Jörg M. Wills 18 Convex Polyhedra Dirichlet Tessellations and Spider Webs. Walter Whiteley with Peter Ash Ethan Bolker and Henry Crapo 19 Uniform Polyhedra from Diophantine Equations. Barry Monson 20 Torus Decompositions of Regular Polytopes in 4 space. Thomas F. Banchoff 21 Tensegrities and Global Rigidity. Robert Connelly 22 Ten Problems in Geometry. Günter Ziegler and Moritz Schmitt Notes and References Sources Acknowledgments and Contributors Index.