Holdings: Abstract regular polytopes

Abstract regular polytopes:

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Bibliographic Details
Main Author:	McMullen, Peter 1942- (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 2002
Edition:	1. publ.
Series:	Encyclopedia of mathematics and its applications 92
Subjects:	Polytopes Polytop Regelmäßiges Polytop
Online Access:	Publisher description Table of contents Inhaltsverzeichnis
Physical Description:	XIII, 551 S. Ill.
ISBN:	0521814960

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adam_text	ENCYCLOPEDIA OE MATHEMATICS AND ITS APPLICATIONS ABSTRACT REGULAR POLYTOPES PETER MCMULLEN UNIVERSITY COLLEGE LONDON EGON SCHULTE NORTHEASTERN UNIVERSITY CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE XIII 1 1 7 15 - 17 21 22 31 39 42 49 60 3 COXETER GROUPS .* 64 3A THE CANONICAL REPRESENTATION 64 3B GROUPS OF SPHERICAL OR EUCLIDEAN TYPE 71 3C GROUPS OF HYPERBOLIC TYPE 76 3D THE UNIVERSAL POLYTOPES {P ,..., P N - ) 78 3E THE ORDER OF A FINITE COXETER GROUP 83 4 AMALGAMATION 95 4A AMALGAMATION OF POLYTOPES 96 4B THE CLASSIFICATION PROBLEM 101 4C FINITE QUOTIENTS OF UNIVERSAL POLYTOPES 103 4D FREE EXTENSIONS OF REGULAR POLYTOPES 106 4E FLAT POLYTOPES AND THE FAP 109 4F FLAT POLYTOPES AND AMALGAMATION 115 1 CLASSICAL REGULAR POLYTOPES 1A IB 1C ID THE HISTORICAL BACKGROUND REGULAR CONVEX POLYTOPES EXTENSIONS OF REGULARITY REGULAR MAPS 2 REGULAR POLYTOPES 2A 2B 2C 2D 2E 2F ABSTRACT POLYTOPES REGULAR POLYTOPES ORDER COMPLEXES QUOTIENTS 1 C-GROUPS PRESENTATIONS OF POLYTOPES X CONTENTS 5 REALIZATIONS 5A REALIZATIONS IN GENERAL 5B THE FINITE CASE 5C APEIROTOPES 6 REGULAR POLYTOPES ON SPACE-FORMS 148 6 A SPACE-FORMS 148 6B LOCALLY SPHERICAL POLYTOPES 152 6C PROJECTIVE REGULAR POLYTOPES 162 6D THE CUBIC TOROIDS 165 6E THE OTHER TOROIDS 170 6F RELATIONSHIPS AMONG TOROIDS 172 6G OTHER EUCLIDEAN SPACE-FORMS 175 6H CHIRAL TOROIDS 177 6J HYPERBOLIC SPACE-FORMS 178 7 MIXING 183 7A GENERAL MIXING 183 7B OPERATIONS ON REGULAR POLYHEDRA 192 7C CUTS 201 7D THE CLASSICAL STAR-POLYTOPES 206^ 7E THREE-DIMENSIONAL POLYHEDRA 217 7F THREE-DIMENSIONAL 4-APEIROTOPES 236 8 TWISTING 244 8A TWISTING OPERATIONS 244 8B THE POLYTOPES L K Q 247 8C THE POLYTOPES 2 K AND 2 K - 9 ^ .. 255 8D, REALIZATIONS OF 2 K AND2 CE ( S) 259 8E A UNIVERSALITY PROPERTY OF C K - 264 8F POLYTOPES WITH SMALL FACES 272 9 UNITARY GROUPS AND HERMITIAN FORMS 289 9A UNITARY REFLEXION GROUPS 290 9B HERMITIAN FORMS AND REFLEXIONS 298 9C GENERAL CONSIDERATIONS 305 9D GENERALIZED TRIANGLE GROUPS . 320 9E TETRAHEDRAL DIAGRAMS * 332 9F CIRCUIT DIAGRAMS WITH TAILS 347 9G ABSTRACT GROUPS AND DIAGRAMS 355 10 LOCALLY TOROIDAL 4-POLYTOPES: I 360 10A GRUNBAUM S PROBLEM 360 10B THE TYPE {4,4,3} 363 10C THE TYPE {4,4,4} 369 10D CUTS FOR THE TYPES {4, 4, R] 378 10E RELATIONSHIPS AMONG POLYTOPES OF TYPE {4, 4, R} 383 CONTENTS XI 11 LOCALLY TOROIDAL 4-POLYTOPES: II 387 11A V THE BASIC ENUMERATION TECHNIQUE 387 11B THE POLYTOPES P T* FI) := {{6, 3} M) , {3, P}} 392 11C POLYTOPES WITH FACETS {6, 3} (JIIS) 400 11D THEPOLYTOPES 6 ^ 0){R0) :={{6,3} ( ,,0), {3,6} (R , 0) } 410 HE THE TYPE {3, 6, 3} 417 1 IF CUTS OF POLYTOPES OF TYPE {6, 3, P] OR {3, 6, 3} 423 11G HYPERBOLIC HONEYCOMBS IN H 3 431 11H RELATIONSHIPS AMONG POLYTOPES OF TYPES {6, 3, P] OR {3, 6, 3} 437 12 HIGHER TOROIDAL POLYTOPES 445 12A HYPERBOLIC HONEYCOMBS IN H 4 AND H 5 445 12B POLYTOPES OF RANK 5 450 12C POLYTOPES OF RANK 6: TYPE {3, 3, 3, 4, 3} 459 12D POLYTOPES OF RANK 6: TYPE {3, 3, 4, 3,3} 462 12E POLYTOPES OF RANK 6: TYPE {3, 4, 3,3,4} 465 13 REGULAR POLYTOPES RELATED TO LINEAR GROUPS 471 13A REGULAR POLYHEDRA 471 13B CONNEXIONS AMONG THE POLYHEDRA 478 13C REALIZATIONS OF THE POLYHEDRA 484 13D THE 4-POLYTOPES 490 13E CONNEXIONS AMONG 4-POLYTOPES 500 14 MISCELLANEOUS CLASSES OF REGULAR POLYTOPES 502 14A LOCALLY PROJECTIVE REGULAR POLYTOPES 502 14B MIXED TOPOLOGICAL TYPES * 509 BIBLIOGRAPHY * ~ 519 INDICES LIST OF SYMBOLS , 539 AUTHOR INDEX . 543 SUBJECT INDEX V 544
any_adam_object	1
author	McMullen, Peter 1942-
author_GND	(DE-588)1097306666
author_facet	McMullen, Peter 1942-
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author_sort	McMullen, Peter 1942-
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building	Verbundindex
bvnumber	BV014359496
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classification_rvk	SK 380
ctrlnum	(OCoLC)48803411 (DE-599)BVBBV014359496
dewey-full	516.3/5
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dewey-tens	510 - Mathematics
discipline	Mathematik
edition	1. publ.
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series	Encyclopedia of mathematics and its applications
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spelling	McMullen, Peter 1942- Verfasser (DE-588)1097306666 aut Abstract regular polytopes Peter McMullen ; Egon Schulte 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2002 XIII, 551 S. Ill. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 92 Polytopes Polytop (DE-588)4175324-0 gnd rswk-swf Regelmäßiges Polytop (DE-588)4177373-1 gnd rswk-swf Polytop (DE-588)4175324-0 s DE-604 Regelmäßiges Polytop (DE-588)4177373-1 s Schulte, Egon Sonstige oth Encyclopedia of mathematics and its applications 92 (DE-604)BV000903719 92 http://www.loc.gov/catdir/description/cam022/2002017391.html Publisher description http://www.loc.gov/catdir/toc/cam024/2002017391.html Table of contents GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009841253&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	McMullen, Peter 1942- Abstract regular polytopes Encyclopedia of mathematics and its applications Polytopes Polytop (DE-588)4175324-0 gnd Regelmäßiges Polytop (DE-588)4177373-1 gnd
subject_GND	(DE-588)4175324-0 (DE-588)4177373-1
title	Abstract regular polytopes
title_auth	Abstract regular polytopes
title_exact_search	Abstract regular polytopes
title_full	Abstract regular polytopes Peter McMullen ; Egon Schulte
title_fullStr	Abstract regular polytopes Peter McMullen ; Egon Schulte
title_full_unstemmed	Abstract regular polytopes Peter McMullen ; Egon Schulte
title_short	Abstract regular polytopes
title_sort	abstract regular polytopes
topic	Polytopes Polytop (DE-588)4175324-0 gnd Regelmäßiges Polytop (DE-588)4177373-1 gnd
topic_facet	Polytopes Polytop Regelmäßiges Polytop
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