Regular complex polytopes
著者
書誌事項
Regular complex polytopes
Cambridge University Press, 1991
2nd ed
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- Frontispiece
- Preface to the second edition
- Preface to the first edition
- 1. Regular polygons
- 2. Regular polyhedra
- 3. Polyhedral kaleidoscopes
- 4. Real four-space and the unitary plane
- 5. Frieze patterns
- 6. The geometry of quaternions
- 7. The binary polyhedral groups
- 8. Unitary space
- 9. The unitary plane, using quaternions
- 10. The complete enumeration of finite reflection groups in the unitary plane
- 11. Regular complex polygons and Cayley diagrams
- 12. Regular complex polytopes defined and described
- 13. The regular complex polytopes and their symmetry groups
- Tables
- Reference
- Index
- Answers to exercises.
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