POLYHEDRA

by Peter Cromwell

compound

Polyhedra have been a part of the fabric of mathematics for two thousand years and have been the inspiration for contributions to many branches of the subject. So it seems remarkable that information concerning their history and mathematical properties is quite difficult to find. The study of polyhedra is still an active area of research and, along with other parts of geometry, is currently enjoying something of a renaissance. This book tells the story of what people have thought about polyhedra over the ages, and explains some of the mathematics that has been developed to study them. It concentrates on the three-dimensional, geometric aspects of the subject since a large part of the attraction of polyhedra derives from making and experimenting with models.

The book is, first and foremost, a mathematics book. However, my aim was to present more than a catalogue of definitions and theorems. The typical textbook style ignores the development of an idea and presents a finished polished product that can leave readers confused by details they see no need for. I wanted to make the mathematics accessible, and also to give the flavour of how mathematics is done. The book is also about the mathematical process and shows how mathematics is developed.

I realised as I was writing the book that it was never going to fall into a standard category. It is not a normal mathematics textbook (though the primary motivation was to collect the mathematics together), but neither is it a popularisation as the mathematics is too advanced. It contains discussion, historical background, and mentions connections with many other disciplines. It is a collection of many things that people can use as a resource in many ways.

A warning

Unfortunately, as the book touches on such a wide variety of topics in the discussion, some reviewers have expected to find more references to their own subjects. For example, a chemist has written:

The idea of writing a really readable book that presents a substantial portion of the history, the lore, the science and the manifold applications of polyhedra is therefore a highly laudable enterprise. This is precisely the task that the author has set himself.

My first comment is that this is not at all the task I set myself. My task was to search out and present in a readable fashion the mathematics of polyhedra. This chemist spends the rest of his review complaining that the book contains mathematics and ignores applications. I do not apologise for this. If you want a book on the applications of polyhedra in chemistry or anywhere else, then write one - I would probably enjoy reading it. Mine is not a book on chemistry, history, crystallography, or numerous other topics.