Polyhedra [Hardcover]

Peter R. Cromwell (Author)

Book Description

ISBN-10: 0521554322 | ISBN-13: 978-0521554329 | Publication Date: June 28, 1997

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.

Editorial Reviews

Review

"The major virtue of the book is that the author has managed to find many interesting paths in mathematics not often traveled." Notices of the AMS

This remarkable book goes far beyond the superficial, providing a solid and fascinating account of the history and mathematics of polyhedra... It is likely to become the classic book on the topic. ...a wonderful book worthy of many readings. It belongs in every university library, and on most mathematicians' book shelves." MAA Online

Book Description

Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics an d group theory. This book 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 presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that might otherwise prove difficult to grasp. Historians of mathematics, as well as those more interested in the mathematics itself, will find this unique book fascinating.

Product Details

• Hardcover: 465 pages
• Publisher: Cambridge University Press (June 28, 1997)
• Language: English
• ISBN-10: 0521554322
• ISBN-13: 978-0521554329
• Product Dimensions: 10 x 7.3 x 1.1 inches
• Shipping Weight: 2.8 pounds
• Average Customer Review: 4.7 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #862,220 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

14 of 14 people found the following review helpful:

5.0 out of 5 stars The _Best_ Polyhedra Book, August 13, 2000

By 

Robert Austin (Conway, AR USA) - See all my reviews

This review is from: Polyhedra (Paperback)

I've read many books on polyhedra, and this is the best I have seen. It covers the history and mathematics of many different polyhedra; the Platonic and Archimedean solids are just the beginning. Kepler's rhombic polyhedra, stellated polyhedra, Miller's solid, etc. -- it's all here. The diagrams are exceptional. I teach high school geometry, and have found this book to be an essential resource in class. The level of detail is quite high, making the book useful as a straight-through read (for someone who is really into math) or a book to flip around in (for those who find heavy math intimidating, but still like polyhedra). Includes helpful tips for model-making. Buy it!

13 of 15 people found the following review helpful:

5.0 out of 5 stars Comprehensive masterpiece!, July 25, 2001

By 

Helmer Aslaksen (Singapore) - See all my reviews
(REAL NAME)   

This review is from: Polyhedra (Paperback)

This is the best book about polyhedra! But it's not always easy to read. He has chosen to take a chronological approach. That means that sometimes you have to look around a bit.

I picked up the book wanting to understand two things.

1. What are the exact definition of the Platonic and Archimedian solids, i.e., how to destinguish the Platonic from the the Deltahedra and the 13 Archimedian from their isomeric forms and the pyramids.

3. What's the reason behind the names for the Kepler-Poinsot solids. Why is the great stellated dodecahedron called the great stellated dodecahedron?

Cromwell answers the first question beautifully in Chapter 2. The second question is first discussed in Chapter 4, but I was still confused. It was only in Chapter 7 that it started to make sense.

I believe the book will answer most of your questions, but you may have to look around for it.

5 of 5 people found the following review helpful:

5.0 out of 5 stars A good treatment of the subject, September 8, 2007

By 

Bruce R. Gilson (Wheaton, MD United States) - See all my reviews
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Amazon Verified Purchase

This review is from: Polyhedra (Paperback)

I really like this book. It would be easy to say it's the best book on the subject that I've seen, but that doesn't say too much, because it's just about the only book I've ever seen devoted exclusively to this subject. So let me say instead that if you are at all interested in the geometric objects known as polyhedra, you will probably find something interesting in this book.

The author deals with the classical geometry of polyhedra, but not exclusively with that aspect. He covers the symmetry properties, best explained in terms of group theory concepts, and introduces and explains the notation of Schoenflies for describing symmetry groups (one of the two most common notations, and the one most used by people interested in things like molecular structure). This makes the book useful as well for those who want to learn about symmetry, and in fact this book is in many ways better for this purpose than many books I have seen with "symmetry" in their titles.

There is one thing with which I find fault: the index is inadequate. I had looked to see whether the book had a section describing the polyhedra known as Johnson solids, and found no reference to either "Norman Johnson" (after whom they are named) or "Johnson solids" in the index. But later, on scanning through the book, I found a very good treatment, explaining Johnson's terminology and with good illustrations of the Johnson solids and related polyhedra. The index made the book appear to be less adequate than it is. If this book ever goes into a second edition, it needs someone to make a new index.