Geometric regular polytopes

by McMullen, Peter

Type Book

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Title Statements

Full title :Geometric regular polytopes / Peter McMullen.

Summary

"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"--

Edition Statements

Publication Date:©2020

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge, United Kingdom
Language:eng
Publication Date:©2020

The Physical Object

Description:1 online resource (xi, 603 pages) : : illustrations.

Edition Identifiers

ISBN:9781108778992, 1108778992
oclc:on1140371645
LC Classification:QA691
Dewey Decimal:516/.158

Euclidean space -- Abstract regular polytopes -- Realizations of symmetric sets -- Realizations of polytopes -- Operations and constructions -- Rigidity -- Classical regular polytopes -- Non-classical polytopes -- General families -- Three-dimensional apeirohedra -- Four-dimensional polyhedra -- Four-dimensional apeirotopes -- Higher-dimensional cases -- Gosset-Elte polytopes -- Locally toroidal polytopes -- A family of 4-polytopes -- Two families of 5-polytopes.