Polyhedra

by Peter R. Cromwell

Polyhedra have cropped up in many different guises throughout recorded history. Recently, polyhedra and their symmetries have been cast in a new light by combinatorics and group theory. This unique text comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics. The author strikes a balance between covering the historical development of the theory surrounding polyhedra and rigorous treatment of the mathematics involved. Attractively illustrated--including 16 color plates--Polyhedra elucidates ideas that have proven difficult to grasp. Mathematicians, as well as historians of mathematics, will find this book fascinating.

Genres: Mathematics, Science

476 pages, Paperback

First published June 28, 1997

Reviews

[Markus Himmelstrand · Rating 4 out of 5]

This book is an excellent example of popular mathematics for the mathematically inclined. Equipped with some familiarity the style of proofs and high school geometry it can effectively be read at the pace of a novel and it is a delightful read.
Written more in the style of an series of essays it covers a wide range of results and types of polyhedra but takes the time to develop most concepts through chronicling their historical evolution starting out with the primitive notions of the Greeks and culminating with modern notions of topology and symmetry being explained using the polyhedrons as examples.
The theorems proven are well chosen and often tie up well

The historical perspective is also refreshing as the connection between individual mathematicians like Archimedes, Kepler, and Cauchy to the different types of polyhedral and results are made. Especially Euler's formula is paid special attention as Cromwell describes 4 different proofs (Euler, Legendre, Cauchy, and von Staudt), their deficiencies, and how they assist in ironing out a more precise definition of what a polyhedron is.

There are also plenty of allusions to real word examples of polyhedra; from occurences in art and architecture to the structures of atoms in solids.

[So Hakim · Rating 4 out of 5]

A pop-math geometry book. Well, not that pop, because there are equations here and there. But if you have good grasp of high school math -- or early college's -- then you should be fine.

[Clara Limón · Rating 5 out of 5]

Quen teña o máis mínimo interese no concepto dos poliedros ten que ter este libro. Moi boas explicacións, un montón de temas distintos, profundiza sobre que implica cada definición, it's soo goood. E aínda por riba ten un montón de ilustracións, o cal é sorprendentemente algo inédito nos libros de xeometría. Collérano na biblio da usc de pasadas a ver se conseguía sacar o traballo de Tato rapidiño, e agora penso en polyhedral croissant constantemente. En serio, nunca lera un libro de mates que disfrutara tanto, I love itt
🥐/🍋 score

[Kacey · Rating 5 out of 5]

This book was a fun trip. It is a history of the subject, a visual appreciation, and a light math book with proofs and exercises. There's chapters on the development of perspective in the Renaissance as well as an introduction to the polyhedral symmetry groups. Because of the varied content and relatively light style of the book it's a surprisingly quick read for a text of this size, even if you complete all the exercises -- most of which can be done in your head if you have good geometric visualization.