Geometric regular polytopes
著者
書誌事項
Geometric regular polytopes
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 172）
Cambridge University Press, 2020
- : hardback
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注記
Includes bibliographical references (p. 583-591) and indexes
内容説明・目次
内容説明
Regular polytopes and their symmetry have a long history stretching back two and a half millennia, to the classical regular polygons and polyhedra. Much of modern research focuses on abstract regular polytopes, but significant recent developments have been made on the geometric side, including the exploration of new topics such as realizations and rigidity, which offer a different way of understanding the geometric and combinatorial symmetry of polytopes. This is the first comprehensive account of the modern geometric theory, and includes a wide range of applications, along with new techniques. While the author explores the subject in depth, his elementary approach to traditional areas such as finite reflexion groups makes this book suitable for beginning graduate students as well as more experienced researchers.
目次
- Foreword
- Part I. Regular Polytopes: 1. Euclidean space
- 2. Abstract regular polytopes
- 3. Realizations of symmetric sets
- 4. Realizations of polytopes
- 5. Operations and constructions
- 6. Rigidity
- Part II. Polytopes of Full Rank: 7. Classical regular polytopes
- 8. Non-classical polytopes
- Part III. Polytopes of Nearly Full Rank: 9. General families
- 10. Three-dimensional apeirohedra
- 11. Four-dimensional polyhedra
- 12. Four-dimensional apeirotopes
- 13. Higher-dimensional cases
- Part IV. Miscellaneous Polytopes: 14. Gosset-Elte polytopes
- 15. Locally toroidal polytopes
- 16. A family of 4-polytopes
- 17. Two families of 5-polytopes
- Afterword
- References
- Symbol index
- Author index
- Subject index.
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