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Polyhedra Paperback – 21 Aug 2008

5.0 out of 5 stars 1 customer review

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Product details

  • Paperback: 476 pages
  • Publisher: Cambridge University Press; First printing of this edition edition (21 Aug. 2008)
  • Language: English
  • ISBN-10: 0521664055
  • ISBN-13: 978-0521664059
  • Product Dimensions: 17.4 x 2.4 x 24.7 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 1,417,993 in Books (See Top 100 in Books)
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Product description


'The topic itself … is easily visualised and it has a long history as part of our culture, interacting with philosophy, art and chemistry. Cromwell's treatment admirably exploits all these opportunities, with many interesting digressions and a lively historical commentary … popular exposition at a high level.' Sir Michael Atiyah, The Times Higher Education Supplement

'… plenty to fascinate.' New Scientist

'… Peter Cromwell has done us a great service by writing this handsome, scholarly and beautifully illustrated book.' Peter Giblin, The London Mathematical Society Newsletter

'This remarkable book goes far beyond the superficial, providing a solid and fascinating account of the history and mathematics of polyhedra, especially regular polyhedra. It is likely to become the classic book on the topic.' MAA Online

' … a fascinating book … the book holds many surprises and will find rich use among students of both mathematics and computer science.' Choice

' … a well got-up book with an abundant and beautiful material of illustration. The study of polyhedra, as the author explicitly states, 'is currently enjoying something of a renaissance'. This work itself will surely help this renaissance, and may be an enjoyable reading for a very wide audience.' Acta. Sci. Math.

' … the book should have a wide and appreciative audience of all ages.' The Times Higher Education Supplement

' … this book contains a thorough treatment of all that is known about polyhedra … A very interesting and detailed account.' European Mathematical Society

' … well-illustrated throughout with line diagrams, as well as several colour plates of the author's own superb models. The writing is clear and entertaining, and reassuringly anticipates many of the reader's questions.' Thomas Bending, The Mathematical Gazette

Book Description

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 explanatory diagrams.

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Top Customer Reviews

Format: Paperback
This book achieves a good balance between very basic definitions of polyhedra, starting with how they were discovered and used in as far back as Ancient Greek civilisation, and then explaining how they can be classified and explored using different mathematical algorithms and axioms. From the cube to the ridiculously complex stellations of the icosahedron, and beyond, this book is ideal for those wishing to explore polyhedra in much more detail, and maybe even do some exploring of their own!
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Most Helpful Customer Reviews on Amazon.com (beta) (May include reviews from Early Reviewer Rewards Program)

Amazon.com: 4.8 out of 5 stars 8 reviews
11 of 12 people found the following review helpful
5.0 out of 5 stars A good treatment of the subject 8 Sept. 2007
By Bruce R. Gilson - Published on Amazon.com
Format: Paperback Verified Purchase
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.
6 of 7 people found the following review helpful
4.0 out of 5 stars History of Polyhedra 24 July 2009
By Atma Weapon - Published on Amazon.com
Format: Paperback Verified Purchase
This book is an excellent thematic history of polyhedra and as the author himself mentions it is not intended to be a catalog, an exposition of theory, or a guide on how to build models. I think it will nevertheless prove interesting not only to the casual reader but also to the hobbyists and mathematicians as there are proofs and exercises and the reader is encouraged to become actively engaged in the topics. I'm mostly a hobbyist but the book seems thorough and well-researched and the author seems to have gone to great lengths to provide context and references for topics not included (e.g. graph theory and combinatorial aspects of polyhedra, polytopes, and so on).

I was disappointed that the "16 color plates" were actually greyscale images and a note directing me to the publisher's website where I could find the actual color images. I guess it's an odd nit to pick but I think the subject is really enhanced by illustrations and color illustrations would have been nice. I can say, though, despite the lack of color, the illustrations are very clear and useful.

I am not sure how to feel about the organization of the book as it's some blend of thematic and chronological. In some ways it feels like it's all over the place and, for example, there are some digressions on art history and perspective that don't seem very crucial. This is reflected in a previous reviewer's comment that it was hard to locate the discussion of Johnson solids. Johnson the person can be found in the name index, but you won't find Johnson solids in the subject index. This brings up another point: the book has a preface, acknowledgments, introduction, appendices, citations, bibliography, name index, and subject index. I'm not sure how to feel about all of this because the organization is necessitated by the vast amount of information (and it's wonderful that it is so informative) and yet it throws me off! Also, I know the author says it's not meant to be a catalog but it would have been really fantastic to have a nice comprehensive catalog (there actually are miniature catalogs in the book but no overarching one). I know you can already find this exact thing online easily enough (and in color!) but it would have been nice to have that in a book.

This is not the only reference you might ever need (especially if you're a hobbyist or academic), but it has tons of information and is worth owning. It's very accessible too so it would make a great gift even for an art student or history buff with an interest in math. I would have loved to have had this book in high school.

I would have awarded five stars if it had color, a comprehensive catalog, or a different organization (or hardback binding!). This book is nevertheless excellent for what it is and if you could only buy one book on polyhedra, this might be your best bet.
4 of 9 people found the following review helpful
4.0 out of 5 stars You should buy this! 19 Nov. 1999
By Tomislav Zule (tomislav.zule@pu.t-com.hr) - Published on Amazon.com
Format: Hardcover Verified Purchase
It's a wonderful book for learning history of polyhedra, but I think it has too little 'mathematics' in. All in all, it's a masterpiece in my mathbook collection.
18 of 19 people found the following review helpful
5.0 out of 5 stars The _Best_ Polyhedra Book 13 Aug. 2000
By Robert Austin - Published on Amazon.com
Format: 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!
14 of 18 people found the following review helpful
5.0 out of 5 stars Comprehensive masterpiece! 25 July 2001
By Helmer Aslaksen - Published on Amazon.com
Format: 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.
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