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Geometric Regular Polytopes

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Geometric Regular Polytopes by Peter McMullen 978-1108489584

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Product details:

  • ISBN 13: 978-1108489584
  • Author: Peter McMullen 
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.

Table contents:

Part I – Regular Polytopes

1 – Euclidean Spacepp 3-62

2 – Abstract Regular Polytopespp 63-93

3 – Realizations of Symmetric Setspp 94-138

4 – Realizations of Polytopespp 139-168

5 – Operations and Constructionspp 169-199

6 – Rigiditypp 200-206

Part II – Polytopes of Full Rankpp 207-208

7 – Classical Regular Polytopespp 209-300

8 – Non-Classical Polytopespp 301-328

Part III – Polytopes of Nearly Full Rankpp 329-330

9 – General Familiespp 331-360

10 – Three-Dimensional Apeirohedrapp 361-382

11 – Four-Dimensional Polyhedrapp 383-430

12 – Four-Dimensional Apeirotopespp 431-449

13 – Higher-Dimensional Casespp 450-474

Part IV – Miscellaneous Polytopespp 475-476

14 – Gosset–Elte Polytopespp 477-505

15 – Locally Toroidal Polytopespp 506-529

16 – A Family of 4-Polytopespp 530-545

17 – Two Families of 5-Polytopes

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