Abstract Regular Polytopes
Edition: 1st edition
Publisher: Cambridge University Press
Published: December 2002
Language: eng
Format: Hardcover
Number of pages: 576
ISBN-13: 9780521814966
Subjects: Combinatorics & graph theory; Geometry; Topology; Polytopes; Analytical Geometry; Mathematics; Science/Mathematics; Applied; Geometry - Algebraic; Mathematics / Applied; Mathematical Analysis
First sentence: Our purpose in this introductory chapter is to set the scene for the rest of the book.
Description: Abstract regular polytopes stand at the end of more than two millennia of geometrical research, which began with regular polygons and polyhedra. They are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties; in many ways more fascinating than traditional regular polytopes and tessellations. The rapid development of the subject in the past 20 years has resulted in a rich new theory, featuring an attractive interplay of mathematical areas, including geometry, combinatorics, group theory and topology. Abstract regular polytopes and their groups provide an appealing new approach to understanding geometric and combinatorial symmetry. This is the first comprehensive up-to-date account of the subject and its ramifications, and meets a critical need for such a text, because no book has been published in this area of classical and modern discrete geometry since Coxeter's Regular Polytopes (1948) and Regular Complex Polytopes (1974). The book should be of interest to researchers and graduate students in discrete geometry, combinatorics and group theory.