Shapes, Space, and Symmetry (Dover Books on Mathematics)

This book is beautiful. It is easy to read and the ideas are beautifully illustrated through photos of models created by the author, a real feat given the 3D subject. A guide for building the models is included; as the author states, the best way to learn about these shapes is to build them. The book carefully and succinctly guides the non-mathematician through fascinating and illuminating transformations of regular polyhedra using their symmetries and duality.For the artist or craftsman who wants to make something inspired by polyhedra, this book is perfect. This is one of my favorite books because every time I pick it up I have a new idea for something to make.

useful for my purpose. If you are very serious about learning about symmetry, be patient with the author and with yourself.

This book illustrates many beautiful ideas through photographs of paper models with concise commentary. First the regular polyhedra, of course, followed by variations of the models that brings out their duality and symmetry properties. We also study how the regular polyhedra can be compounded, inscribed in each-other, and pasted together along a common cross-section ("when halves of the Platonic solids having the same cross-sections come together, monsters are born"). We also study truncating the regular polyhedra to obtain the semi-regular polyhedra, stellating to obtain non-convex regular solids, and faceting to obtain non-convex semi-regular polyhedra. There is a deplorably short but somewhat useful section with practical advice on building models. "Suitable cardboard is of the sort used for mounting photographs, and suitable glue is a 'white glue' of the sort exemplified by 'Elmer's Glue-all' ... For several hours the joints remain sufficiently flexible to permit adjustment of the dihedral angle". It's a pity that we are advised to construct the sides of the regular polyhedra by unromantic means; equilateral triangles are to be made using "a draftsman's 30-60-90 triangle" and the construction of a regular pentagon "requires a guide made of heavier cardboard, such as an illustration board, with two edges meeting at the desired angle"---obviously you will want to construct the faces using ruler-and-compass constructions.

I love this book. I got it thinking I wouldn’t like it and was pleasantly surprised by how good it is. The concepts covered are well explained both with words and visuals and the concepts covered flow coherently throughout the whole book. One I am proud to have in my geometry collection.

This is a fascinating book if you're doing a deep dive on geometry. Good complement to Synergetics and a fantastic addition for anybody with a 3d printer. I was personally interested in the concept of "nolids" and this book describes them in some detail. I was so happy with this book, I bought a copy for a friend as a gift.

Filled with photos and good information on polyhedra. Since most math courses in high school do not discuss these shapes, this book was perfect for learning about the topic.

Detailed text, many photographs of a large collection of well made models and clear figures bound together by concise, casual text. If you are interested in solid geometry for any reason, this book belongs in your collection.

gave me a much better understanding of the variety of 3D forms. Very methodical. Shame the cover doesnt do it justice. Look inside !