Geometric Regular Polytopes (Encyclopedia of Mathematics and its Applications)

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.

Peter McMullen is Professor Emeritus of Mathematics at University College London. He was elected a foreign member of the Austrian Academy of Sciences in 2006 and is also a member of the London Mathematical Society and the European Mathematical Society. He was elected a Fellow of the American Mathematical Society in 2012. He has co-edited several books and co-authored Abstract Regular Polytopes (Cambridge, 2002). His work has been discussed in the Encyclopaedia Britannica and he was an invited speaker at the International Congress of Mathematicians in 1974.