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. 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
1 online resource (x, 341 pages :) : illustrations
9780387927138, 9780387927145, 0387927131, 038792714X
846987605
Print version:
Introduction to the Polyhedron Kingdom / Marjorie Senechal
Six Recipes for Making Polyhedra / Marion Walter, Jean Pedersen, MagnusWenninger, Doris Schattschneider, Arthur L. Loeb, Eric Demaine, Martin Demaine, and Vi Hart
Regular and Semiregular Polyhedra / H.S.M. Coxeter
Milestones in the History of Polyhedra / Joseph Malkevitch
Polyhedra: Surfaces or Solids? / Arthur L. Loeb
Dürer's Problem / Joseph O'Rourke
Exploring the Polyhedron Kingdom / Marjorie Senechal
Spatial Perception and Creativity / Janos Baracs
Goldberg Polyhedra / George Hart
Polyhedra and Crystal Structures / Chung Chieh
Polyhedral Molecular Geometries / Magdolna Hargittai and Istvan Hargittai
Form, Function, and Functioning / George Fleck
The Polyhedron Kingdom Tomorrow / Marjorie Senechal
Paneled and Molecular Polyhedra: How Stable Are They? / Ileana Streinu
Duality of Polyhedra / Banko Grünbaum and G.C. Shephard
Combinatorial Prototiles / Egon Schulte
Polyhedra Analogues of the Platonic Solids / Jörg M. Wills
Convex Polyhedra, Dirichlet Tessellations, and Spider Webs / Walter Whiteley with Peter Ash, Ethan Bolker, and Henry Crapo
Uniform Polyhedra from Diophantine Equations / Barry Monson
Torus Decompositions of Regular Polytopes in 4-space / Thomas F. Banchoff
Tensegrities and Global Rigidity / Robert Connelly
Ten Problems in Geometry / Günter Ziegler and Moritz Schmitt