Abstract Regular Polytopes

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.

First Sentence

Our purpose in this introductory chapter is to set the scene for the rest of the book.

Subjects

Other Editions

• Abstract Regular PolytopesHardcoverCambridge University Press2002-12-01
• Abstract Regular PolytopesCambridge University Press2002-01-01
• Abstract Regular PolytopesCambridge University Press2002-01-01
• Abstract Regular PolytopesCambridge University Press2002-01-01
• Abstract Regular PolytopesCambridge University Press2004-01-01
• Abstract Regular PolytopesCambridge University Press2009-01-01