- 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)
- See Complete Table of Contents
Polyhedra Paperback – 21 Aug 2008
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'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
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.
Top Customer Reviews
Most Helpful Customer Reviews on Amazon.com (beta) (May include reviews from Early Reviewer Rewards Program)
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.
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.
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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