Regular Polytopes

by H.S.M. Coxeter

Polytopes are geometrical figures bounded by portions of lines, planes, or hyperplanes. In plane (two dimensional) geometry, they are known as polygons and comprise such figures as triangles, squares, pentagons, etc. In solid (three dimensional) geometry they are known as polyhedra and include such figures as tetrahedra (a type of pyramid), cubes, icosahedra, and many more; the possibilities, in fact, are infinite! H. S. M. Coxeter's book is the foremost book available on regular polyhedra, incorporating not only the ancient Greek work on the subject, but also the vast amount of information that has been accumulated on them since, especially in the last hundred years. The author, professor of Mathematics, University of Toronto, has contributed much valuable work himself on polytopes and is a well-known authority on them.
Professor Coxeter begins with the fundamental concepts of plane and solid geometry and then moves on to multi-dimensionality. Among the many subjects covered are Euler's formula, rotation groups, star-polyhedra, truncation, forms, vectors, coordinates, kaleidoscopes, Petrie polygons, sections and projections, and star-polytopes. Each chapter ends with a historical summary showing when and how the information contained therein was discovered. Numerous figures and examples and the author's lucid explanations also help to make the text readily comprehensible.
Although the study of polytopes does have some practical applications to mineralogy, architecture, linear programming, and other areas, most people enjoy contemplating these figures simply because their symmetrical shapes have an aesthetic appeal. But whatever the reasons, anyone with an elementary knowledge of geometry and trigonometry will find this one of the best source books available on this fascinating study.

Genres: Mathematics, Geometry, Reference

565 pages, Kindle Edition

First published June 1, 1973

About the author

Harold Scott MacDonald "Donald" Coxeter (1907-2003), CC, FRS, FRSC was a British and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th century.

Reviews

[Chris · Rating 4 out of 5]

Non-mathematicians would be surprised to learn about Coxeter's kaleidoscope of high-dimensional crystals.

For mathematicians this is a must-own.

By the way, Coxeter was racist.

[Røbert · Rating 3 out of 5]

I bought this from an interest in pattern and polyhedra as it is an established classic, delving into higher dimensions. I can't deny that it is classic and definitive, but it is very much a textbook aimed at those doing maths as a career or postgraduate study. For my purposes, half an hour on wikipedia was more fruitful to get a practical on-hands overview of higher dimensional polytopes.

[Ted]

Great book on multidimensional geometry!

[James Jennings · Rating 5 out of 5]

A rather dry and dense mathematics text, with lots of information not available in any other single source. I loved it.

[Yashwant Chauhan · Rating 5 out of 5]

For this alone: "... in attempting to do so, however, we seem to peep through a chink in the wall of our physical limitations, into a new world of dazzling beauty. Such an escape from the turbulence of ordinary life will perhaps help to keep us sane."

[Mi Lia · Rating 5 out of 5]

A classic.