Shapes, Space, and Symmetry (Paperback)

~ (Author)

Editorial Reviews

Product Description

Aimed at the layman as well as the student or professional in mathematics, this book explains the structure of the nine regular solids—tetrahedron, cube, octahedron, dodecahedron, icosahedron among them—as well as many semiregular solids, and demonstrates how they can be used to explain mathematics visually rather than by symbol systems. Instructions for constructing cardboard models of each. Over 300 photographs and drawings. Index.

Product Details

• Paperback: 208 pages
• Publisher: Dover Publications (September 19, 1991)
• Language: English
• ISBN-10: 0486268519
• ISBN-13: 978-0486268514
• Product Dimensions: 8.8 x 5.9 x 0.6 inches
• Shipping Weight: 10.4 ounces
• Average Customer Review: 4.8 out of 5 stars  See all reviews (5 customer reviews)
• Amazon.com Sales Rank: #634,310 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

52 of 54 people found the following review helpful:

5.0 out of 5 stars A beautiful, simple and elegant book on polyhedra, November 1, 1998

By	Hop David (Ajo, Arizona) - See all my reviews

A friend of mine lent me this book in 1975. (I still haven't given it back). Although this 200 page book is very simply and clearly written, I have never been able to sit down and read it from start to finish. Each part I read makes me stop and contemplate. After 24 years I still find new things in it! The book starts out describing the five Platonic solids. Next it explores the dualities: between the octahedron and cube, between the dodecahedron and icosohedron, and between the tetrahedron with itself. Holden talks about solids discovered by Kepler and Poinsot, space filling solids other than the cube, Nolids, lattices and a whole lot more. He also describes how to make your own models with cardboard and Elmers' glue. Doug Kendall's photographs of Holden's models are very pleasing. This is my favorite book.

23 of 23 people found the following review helpful:

5.0 out of 5 stars Little Gem, January 18, 2002

By	Andrew MacDonald (Seattle, WA USA) - See all my reviews

Alan Holden must be a very dedicated man. This short book on polyhedra is filled with pictures of intricate paper models, all made by the author. In the final section, showing how to construct similar models, one can see a photo of his workshop with hundreds of models arrayed neatly on shelves behind him. This book was clearly a work of love.

Most of the book is occupied with a treatment of regular and semiregular polyhedra, prisms and antiprisms. These are examined in some depth--for example, all nine regular polyhedra are constructed. The last fifty pages introduce other topics, such as packing, lattices, and knots; the treatment here is very brief, somewhat disappointing and leaving a desire for more depth. The same can be said of the final section, on construction--Holden gives general guidelines but leaves the reader to compute the dimensions of all the faces of his models himself.

The prose is clear and concise, rare for a mathematics book. But the real substance lies in the photographs of polyhedra models. These are contructed in such a way that it is always easy to see the details of the solid: faces of different shapes are made of different shades of paper, complicated models are shown in intermediate stages of construction, polyhedra to be compared (such as duals) are shown as individuals and interpenetrating. The great icosidodecahedron photo on page 112 (or its companion that might go by the same name on page 98) is almost worth the price of the book by itself.

This is not a rigorous treatment of the subject, but it is a beautiful one.

15 of 15 people found the following review helpful:

5.0 out of 5 stars An excellent introduction to Archimedean Star Polyhedra, February 13, 2001

By	Donald Rogers (Seattle, WA United States) - See all my reviews (REAL NAME)

This well-made and inexpensive book is brim-full of pictures of Alan Holden's models of polyhedra. It is a book for the hobbyist and the enthusiastic closet Pythagorean, more than it is for the professional mathematician. It is especially useful as an introduction to Archimedean star polyhedra, which are surely as beautiful as anything in geometry, and which were not fully catalogued until the 1950s.

If you find this material as compellingly fascinating as I do, you may want to follow up this book with these two:

"Polyhedron Models," by Magnus Wenninger, has a more thorough and systematic treatment of the Archimedean star polyhedra than Holden's book. These include some incredibly complicated models of "snub" star polyhedra -- spectacular stuff that is not included here. (On the other hand, Wenninger's book costs a good deal more.)

"Regular Polytopes," by H.S.M. Coxeter, is an elegantly written introduction to polyhedra in 3 and 4 dimensions. Coxeter himself wrote the first systematic treatment of the Archimedean star-polyhedra, and helped to discover the last few in the process. This book's illustrations are nowhere near as nice as the other ones', but this is balanced by its more rigorous mathematical treatment of the theme. Somebody needs to come up with a better way (using computer graphics?) to illustrate higher-dimensional polyhedra. In the meantime, this inexpensive book is the best I know on the subject.