The properties of regular solids exercise a fascination which often appeals strongly to the mathematically inclined, whether they are professionals, students or amateurs. In this classic book Professor Coxeter explores these properties in easy stages, introducing the reader to complex polyhedra (a beautiful generalization of regular solids derived from complex numbers) and unexpected relationships with concepts from various branches of mathematics: magic squares, frieze patterns, kaleidoscopes, Cayley diagrams, Clifford surfaces, crystallographic and non-crystallographic groups, kinematics, spherical trigonometry, and algebraic geometry. In the latter half of the book, these preliminary ideas are put together to describe a natural generalization of the Five Platonic Solids. This updated second edition contains a new chapter on Almost Regular Polytopes, with beautiful 'abstract art' drawings. New exercises and discussions have been added throughout the book, including an introduction to Hopf fibration and real representations for two complex polyhedra.
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The properties of polytopes, the four-dimensional analog of polyhedra, exercise an intellectual fascination that appeals strongly to the mathematically inclined, whether they are professionals, students or amateurs. In this classic book, Professor Coxeter explores these properties in easy stages introducing the reader to complex polytopes (a beautiful generalization of regular solids derived from complex numbers) and the unexpected relationships that complex polytopes have with concepts from various branches of mathematics. In the first half of the book the author discusses magic squares, frieze patterns, kaleidoscopes, Cayley diagrams, Clifford surfaces, non-crystallographic groups, kinematics, spherical trigonometry, and algebraic geometry. Later these ideas are assembled to describe a natural generalization of the Five Platonic Solids. The fully updated second edition contains a new chapter on "Almost Regular Polytopes" and beautiful abstract art drawings. In addition, new exercises and discussions, including an introduction to Hopf fibration and real representations for two complex polyhedra, supplement the text. -- Book Description
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Hardcover. Second edition. 25.5 x 28.5 cm. 210pp. Black cloth in dust jacket. Equations, figures, problems and solutions, index. Originally done in 1974, this is the second edition done in 1991 which has a new chapter on Almost Regular Polytopes. Near Fine in Near Fine dust jacket. Seller Inventory # 79182
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Large Hardcover. Condition: Very Good. Dust Jacket Condition: Very Good. Second Edition. Second edition. Jacket edges bumped. Boards soiled. 1991 Large Hardcover. xiv, 210 pp. The properties of regular solids exercise a fascination which often appeals strongly to the mathematically inclined, whether they are professionals, students or amateurs. In this classic book Professor Coxeter explores these properties in easy stages, introducing the reader to complex polyhedra (a beautiful generalization of regular solids derived from complex numbers) and unexpected relationships with concepts from various branches of mathematics: magic squares, frieze patterns, kaleidoscopes, Cayley diagrams, Clifford surfaces, crystallographic and non-crystallographic groups, kinematics, spherical trigonometry, and algebraic geometry. In the latter half of the book, these preliminary ideas are put together to describe a natural generalization of the Five Platonic Solids. This updated second edition contains a new chapter on Almost Regular Polytopes, with beautiful 'abstract art' drawings. New exercises and discussions have been added throughout the book, including an introduction to Hopf fibration and real representations for two complex polyhedra. Seller Inventory # 2332338
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