Customer Reviews

Polyhedra

5 star:		(5)
4 star:		(2)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

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!

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.

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.

you like polyhedra, so buy this book. that is why it exists.
i have enjoyed this book for years and used parts of it for my university students.
a classic.

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.

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.

".....Historians of mathematics as well as those more interested in the mathematics itself, WILL FIND THIS UNIQUE BOOK RICHLY REWARDING."
[from the book of the back cover]