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Abstract Regular Polytopes Encyclopedia of Mathematics and its Applications 92 1st Edition by Peter Mcmullen, Egon Schulte ISBN 0521814960 978-0521814966

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Abstract Regular Polytopes Encyclopedia of Mathematics and its Applications 92 1st Edition Peter Mcmullen Digital Instant Download

Author(s): Peter McMullen, Egon Schulte
ISBN(s): 9780521814966, 0521814960
Edition: 1st
File Details: PDF, 2.76 MB
Year: 2002
Language: english
SKU: EB-2021294 Category: Tags: ,

Abstract Regular Polytopes Encyclopedia of Mathematics and its Applications 92 1st Edition by Peter Mcmullen, Egon Schulte – Ebook PDF Instant Download/Delivery:  0521814960, 978-0521814966
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Product details: 

ISBN 10:  0521814960

ISBN 13:  978-0521814966

Author:  Peter Mcmullen, Egon Schulte

Abstract regular polytopes stand at the end of more than two millennia of geometrical research, which began with regular polygons and polyhedra. The rapid development of the subject in the past twenty years has resulted in a rich new theory featuring an attractive interplay of mathematical areas, including geometry, combinatorics, group theory and topology. This is the first comprehensive, up-to-date account of the subject and its ramifications. It meets a critical need for such a text, because no book has been published in this area since Coxeter’s “Regular Polytopes” (1948) and “Regular Complex Polytopes” (1974).
 

Table of contents: 

1 Classical Regular Polytopes

1A The Historical Background

Regular Convex Polytopes 1B

1C Extensions of Regularity

1D Regular Maps

2 Regular Polytopes

2A Abstract Polytopes

2B Regular Polytopes

2C Order Complexes

2D Quotients

2E C-Groups

2F Presentations of Polytopes

3 Coxeter Groups

3A The Canonical Representation

3B Groups of Spherical or Euclidean Type

3C Groups of Hyperbolic Type

3D The Universal Polytopes {P1,…, Pn-1}

3E The Order of a Finite Coxeter Group

4 Amalgamation

4A Amalgamation of Polytopes

4B The Classification Problem

4C Finite Quotients of Universal Polytopes

4D Free Extensions of Regular Polytopes

4E Flat Polytopes and the FAP

4F Flat Polytopes and Amalgamation

5 Realizations

5A Realizations in General

5B The Finite Case

5C Apeirotopes

6 Regular Polytopes on Space-Forms

6A Space-Forms

6B Locally Spherical Polytopes

6C Projective Regular Polytopes

6D The Cubic Toroids

6E The Other Toroids

6F Relationships Among Toroids

6G Other Euclidean Space-Forms

6H Chiral Toroids

6J Hyperbolic Space-Forms

7 Mixing

7A General Mixing

7B Operations on Regular Polyhedra

7C Cuts

7D The Classical Star-Polytopes

7E Three-Dimensional Polyhedra

7F Three-Dimensional 4-Apeirotopes

8 Twisting

8A Twisting Operations

8B The Polytopes CK.G

8C The Polytopes 2 and 25.9(s)

8D Realizations of 2 and 2K,G(s)

8E A Universality Property of CK.G

8F Polytopes with Small Faces

9 Unitary Groups and Hermitian Forms

9A Unitary Reflexion Groups

9B Hermitian Forms and Reflexions

9C General Considerations

9D Generalized Triangle Groups

9E Tetrahedral Diagrams

9F Circuit Diagrams with Tails

9G Abstract Groups and Diagrams

10 Locally Toroidal 4-Polytopes: I

10A Grünbaum’s Problem

10B The Type (4,4,3}

10C The Type {4,4,4}

10D Cuts for the Types (4, 4, r}

10E Relationships Among Polytopes of Type (4, 4, r)

11 Locally Toroidal 4-Polytopes: II

11A The Basic Enumeration Technique

11B The Polytopes pT(0):= {{6,3}(5.0), (3, p}}

11C Polytopes with Facets (6,3)(5.3)

11D The Polytopes 6T 67(5.0).(1.0):= {{6, 3](5.0), (3, 6)(1,0)}

11E The Type {3, 6, 3}

11F Cuts of Polytopes of Type (6, 3, p} or {3, 6, 3)

11G Hyperbolic Honeycombs in H³

11H Relationships Among Polytopes of Types {6, 3, p} or {3, 6, 3}

12 Higher Toroidal Polytopes

12A Hyperbolic Honeycombs in H¹ and H³

12B Polytopes of Rank 5

12C Polytopes of Rank 6: Type (3, 3, 3, 4, 3)

12D Polytopes of Rank 6: Type {3, 3, 4, 3, 3)

12E Polytopes of Rank 6: Type (3, 4, 3, 3, 4)

13 Regular Polytopes Related to Linear Groups

13A Regular Polyhedra

13B Connexions Among the Polyhedra

13C Realizations of the Polyhedra

13D The 4-Polytopes

13E Connexions Among 4-Polytopes

14 Miscellaneous Classes of Regular Polytopes

14A Locally Projective Regular Polytopes

14B Mixed Topological Types

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Tags: Peter Mcmullen, Egon Schulte, Abstract Regular, Polytopes Encyclopedia, its Applications