Regular Complex Polytopes - Hardcover

Coxeter, H. S. M.

Hardcover

ISBN 10: 0521394902 ISBN 13: 9780521394901

Publisher: Cambridge University Press, 1991

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.

Review:

..".of major interest to geometers, but the ordinary (perhaps even nonmathematical) reader will derive pleasure from the many beautiful pictures which it also includes." P. McMullen, Mathematical Reviews