Donald Coxeter infused enthusiasm, even passion, for mathematics in people of any age, any background, any profession, any walk of life. Enchanted by Euclidean geometry, he was interested in the beauty, the description, and the exploration of the world around us. His involvement in art and with artists earned him admiration and friends in the intellectual community all over the globe. Coxeter's devotion to polytopes and his interest in the theory of configurations live on in his students and followers.Coxeter groups arise in various subjects in applied mathematics, and they have a permanent place in some of the most demanding and fascinating branches of abstract mathematics, such as Lie algebras, algebraic groups, Chevalley groups, and Kac-Moody groups. This collection of articles by outstanding researchers and expositors is intended to capture the essence of the Coxeter legacy. It is a mixture of surveys, up-to-date information, history, storytelling, and personal memories; and it includes a rich variety of beautiful illustrations.
The isomorphism problem for Coxeter groups by B. Muhlherr Coxeter theory: The cognitive aspects by A. V. Borovik From Galois and Lie to Tits buildings by M. Ronan The Coxeter element and the branching law for the finite subgroups of $SU(2)$ by B. Kostant Hyperbolic Coxeter groups and space forms by R. Kellerhals Regular and chiral polytopes in low dimensions by P. McMullen and E. Schulte Polytopes, honeycombs, groups and graphs by B. Monson and A. I. Weiss Equivelar polyhedra by J. M. Wills Combinatorics of sections of polytopes and Coxeter groups in Lobachevsky spaces by A. Khovanskii Donald and the golden rhombohedra by M. Senechal Configurations of points and lines by B. Grunbaum Meditations on Ceva's theorem by J. Richter-Gebert Coxeter and the artists: Two-way inspiration by D. Schattschneider The visual mind: Art, mathematics and cinema by M. Emmer.