PlatonicSolids.info

Annotated Bibliography

Welcome to the Platonic Solids Information Site annotated bibliography page! I have assembled here what I believe to be the most important books on the subject. If you have any other books to suggest, please send me an email, and I will be glad to consider them for inclusion.

A note about the links: Each book title contains a hyperlink to Amazon.com. Of course, you are welcome to buy your books from the merchant of your choice, or even to just order them from the library. The links are included for several reasons. First, Amazon is a convenient place to find out more about the book such as what others say about it or what some of the interior pages look like. Second, you may find that Amazon is a convenient place to shop for books. And lastly, if you buy a book or anything from Amazon after following a link on this page, a small percentage comes back to support my work.

If you would like to go to a custom Amazon store that contains all of these titles and nothing else,
click on this link -->>> The Platonic Solids Information Site Bibliography Amazon Bookstore

The Books:

Dome Notes by Peter Hjersman

As some of us remember, “The Sixties” really happened in the seventies.  Thanks to the work of R. Buckminster Fuller, three-dimensional geometry played an important role in the new counterculture in the form of geodesic dome architecture.  Dome Notes, published in 1975, is an in-depth encyclopedia of the mathematics and mechanics behind the geodesic dome movement.  It does all of this in a package that has the grassroots feel of The Whole Earth Catalog.  For more of the same, look for the various versions of DomeBook.

 

Fantasia Mathematica by Clifton Fadiman

This is a wonderful book of stories and essays set in mathematical contexts.  You don’t need to be a mathematician to be delighted by these writings.  One of my favorites is "-And He Built a Crooked House," by Robert Heinlein.  This story does a great job helping the lay reader understand four-dimensional geometry.

Flatland: A Romance of Many Dimensions by Edwin A. Abbott

Written in 1884, Flatland is still one of the best books for anyone wishing to understand the concept of dimension.  This entertaining social satire is a must-read for anyone interested in dimensions.  The story takes place in worlds with two, one, and zero dimensions but the insights gained allow the reader to consider worlds with four or more dimensions.

 

Journey through Genius: The Great Theorems of Mathematics by William Dunham

This book takes the reader through the major developments in mathematics starting in 440 B.C. and ending in 1891 A.D.  This book is as much about the mathematicians as it is about the mathematics.  The reader gets to know the characters, their personalities, and the challenges they faced (interpersonal, political, academic, and mathematical).  The reader gets to meet Euclid, Archimedes, Newton, the Bernoullis, and Euler to name a few.

 

Platonic & Archimedean Solids by Daud Sutton

This beautiful, simple, elegant little book lays out all of the properties of and relationships among the various geometric solids in a concise and organized manner.  This book is easy to follow for anyone with an interest in the subject.

The Platonic Solids Book by Dan Radin

This is the book version of this website.

Platonic Solid Rock video by Dan Radin

This is the video that started this entire site. Definitely check it out if you haven't already!

Polyhedra by Peter R. Cromwell

Cromwell covers every aspect of polyhedra.  He traces the history of this branch of mathematics to every corner of the globe and every aspect of life.  He also presents the mathematics in a thorough yet accessible manner.

Polyhedron Models by Magnus J. Wenninger

This is a complete and detailed manual for building models of a wide variety of polyhedra.  With its beautiful photographs and attention to detail, this is considered the most complete and important text on the subject.  However, this is not a book on paper folding; the models are all made from individual faces meticulously glued together.  Still, if you are looking to create physical models of polyhedra, this is the number one recommended manual.

Polyhedron Origami for Beginners by Miyuki Kawamura

This beautifully illustrated manual contains clear, easy-to-follow, step-by-step instructions for creating an assortment of origami polyhedra in solid as well as skeletal and outline forms.  Some purists may object to the fact that many of the constructions require glue, but I believe the quality of the results and the simplicity of the instructions far outweigh this objection.

Proofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos

This amazing book is written in the form of a play that takes place in a classroom.  It is the basis of the Proof?! section of this website.  While examining Euler’s theorem of polyhedra, the students and teacher dissect the philosophical underpinnings of concepts such as proof, theorem, and mathematical truth.  This is an insightful and entertaining masterpiece.

Regular Polytopes by H. S. M. Coxeter

Coxeter’s 1963 treatise is the definitive source for polyhedral mathematics.  If you are interested in the hardcore mathematics behind the shapes, you must read this book.

Shapes, Space, and Symmetry by Alan Holden

This book not only describes the solids and their relationships, but it also contains photographs of the author's beautiful models.  The book includes instructions for how to make the models yourself.  This is a must-have for anyone interested in building polyhedral models.

Timaeus and Critias by Plato

Plato’s dialogue, Timaeus (360 B.C.) is the reason for the name, “Platonic Solids.”  In this dialogue, Plato proposes what I believe to be a precursor to molecular chemistry.  Plato states that all matter is made up of different combinations of smaller basic building blocks in the shapes of the five perfect forms, the Platonic Solids.  The qualities of each substance are derived from the substance's unique combination of the five basic shapes.  Each shape imparts its own special attribute, specifically Earth, Air, Fire, Water, or Cosmos.

Zome Geometry: Hands-on Learning with Zome Models by George W. Hart

In this extensive polyhedral geometry workbook, Mr. Hart covers the mathematics of three-dimensional solids through model building with an ingenious manipulative system called Zometools.  See the Links page of this website to appreciate Mr. Hart’s mastery of the subject of polyhedral mathematics and sculpture.  If you would like to see his latest project, visit the new Museum of Mathematics.

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This site and all of its contents were created by Dan Radin unless otherwise stated.