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Index
Preface
Introduction
C HAPTER 1
Leonhard Euler and His Three “Great” Friends
C HAPTER 2
What Is a Polyhedron?
C HAPTER 3
The Five Perfect Bodies
C HAPTER 4
The Pythagorean Brotherhood and Plato’s Atomic Theory
C HAPTER 5
Euclid and His Elements
C HAPTER 6
Kepler’s Polyhedral Universe
C HAPTER 7
Euler’s Gem
C HAPTER 8
Platonic Solids, Golf Balls, Fullerenes, and Geodesic Domes
C HAPTER 9
Scooped by Descartes?
C HAPTER 10
Legendre Gets It Right
C HAPTER 11
A Stroll through Königsberg
C HAPTER 12
Cauchy’s Flattened Polyhedra
C HAPTER 13
Planar Graphs, Geoboards, and Brussels Sprouts
C HAPTER 14
It’s a Colorful World
C HAPTER 15
New Problems and New Proofs
C HAPTER 16
Rubber Sheets, Hollow Doughnuts, and Crazy Bottles
C HAPTER 17
Are They the Same, or Are They Different?
C HAPTER 18
A Knotty Problem
C HAPTER 19
Combing the Hair on a Coconut
C HAPTER 20
When Topology Controls Geometry
C HAPTER 21
The Topology of Curvy Surfaces
C HAPTER 22
Navigating in n Dimensions
C HAPTER 23
Henri Poincaré and the Ascendance of Topology
E PILOGUE
The Million-Dollar Question
Acknowledgements
Appendix A
Build Your Own Polyhedra and Surfaces
Appendix B
Recommended Readings
Notes
References
Illustrations Credits
Index
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