A fascinating collection of geometric proofs and properties.

This collection of essays on the legacy of mathematican Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths.

This unabridged paperback edition contains complete coverage, ranging from topics in the Euclidean plane to affine geometry, projective geometry, differential geometry and topology.

The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems.

And as Siobhan Roberts elegantly conveys in The King of Infinite Space, there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century.

A current, furthermore, which has not been constant. In the 1930s, after a period of pervasive prominence, it appeared to be in decline, even passe. These same years were those in which H. S. M. Coxeter was beginning his scientific work.

This book is being published in conjunction with the 50th anniversary of the Canadian Mathematical Society and it is a collection of 26 papers written by Dr. Coxeter.

This classic work offers scores of stimulating, mind-expanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, map-coloring problems, cryptography and cryptanalysis, much more.

... Coxeter himself. For instance, the enumeration of all finite Coxeter groups was first provided by Coxeter in one of the earliest papers written on the subject ([Coxeter (1935)]). Following the lead established by Coxeter's initial ...

Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book.