Geometry is the most fundamental subject in the universe, for it describes the relationships within and between all things.

Discover the simple but powerful mathematics of the underlying geometric figures that shape our world.

What's New in the Second Edition

  • Analysis of a new polyhedron, the truncated icosahedron, or Bucky Ball (soccer ball).
  • Addition of a section on "Phi math," used extensively throughout the book. Phi has amazing properties of reduction and combination. Simplification of several ``Phi math'' equations.
  • Re-labeling of several figures in the first two chapters for clarity.
  • Simplification of two sections of the Rhombic Dodecahedron chapter for greater clarity.
  • Simplification of a section in the Decagon appendix for greater clarity.
  • Correction of several typos in the First Edition.
  • Clickable Table of Contents. All images are linked within the document for easy access. All sections bookmarked for easy reference in the free Adobe reader.
  • Can be read in the browser or in the free Acrobat Reader. Right click on an image and select "Open in new tab" to pop the image out of the book. This feature makes it easier to use with the zometool.

Can geometry be exciting?

It can for those who can appreciate the beauty of numbers and their relationships.

This eBook contains a meticulous geometric investigation of the 5 Platonic Solids and 6 other important polyhedra, as well as reference charts for each solid.

Poly (many) hedron (face) means "many faces." Polyhedra are 3 dimensional figures with 4 or more faces, or sides.

These polyhedra are reflections of Nature herself, and a study of them provides insight into the way the world is structured.

Nature is not only beautiful, but highly intelligent. As you explore the polyhedra in this book, this will become apparent over and over again.

The eBook contains a geometric explanation of the Phi Ratio and Fibonacci series, and a detailed analysis of the pentagon, which forms the basis for many of these solids. The pentagon is composed entirely of Phi relationships, and is integral to a proper understanding of sacred geometry.

With over 160 illustrations , this eBook is perfect for teachers and students of geometry alike. It is a must for those who are serious about sacred geometry. Almost all of the diagrams use scalable vector graphics, which means they will display clearly at all resolutions.
This book is dedicated to those who can appreciate the logic of numbers and the beauty of nature, for they are both aspects of the same unifying principle.

Prerequisites: Requires a knowledge of simple algebra and elementary trigonometry. No brainiac math skills required! Only the ability to appreciate nature's own logic.

The Second Edition contains an additional polyhedron, the Truncated Icosahedron, or Soccer Ball, as well as several sections that have been rewritten to provide easier reading.

"Dear Ken: Received your Geometry book this weekend, and it is really a very interesting, and also fascinating book. This complex solid geometry is presented in such an understanding format"
Robert Sebrosky, Charlotte, NC

A Geometric Analysis of the Platonic Solids and other Semi-Regular Polyhedra, Second Edition (eBook)

presents a detailed analysis of the five Platonic Solids:

  • The Tetrahedron
  • The Octahedron
  • The Cube
  • The Icosahedron
  • The Dodecahedron

Along with six other important polyhedra:

  • The Cube Octahedron
  • The Rhombic Dodecahedron
  • The Rhombic Triacontahedron
  • The Icosa Dodecahedron
  • The Star Tetrahedron
  • The Truncated Icosahedron (soccer ball)

We also thoroughly investigate the pentagon, which is nature’s key to unlocking the secrets of the Platonic Solids, and delve into the Phi Ratio, which turns up over and over again in these figures.

The Rhombic Triacontahedron, for example, is nature's way of nesting the five Platonic Solids elegantly within one structure. The analysis of this polyhedron alone is worth the price of the book!

The book also contains an introduction to a new kind of math, which I call Phi math. Phi is the representation of perfect harmony. Math based on Phi has fascinating properties.


This eBook contains a fully linked PDF file to all geometric diagrams and important text links and is typeset in LaTeX, the world's premier typesetting program. All geometric diagrams are finely-detailed SVG images that can be expanded for close viewing in the free Acrobat DC Reader.

$12.99: Linked PDF file. Click on "Add to Cart" button


(To purchase the book in soft cover edition, Click Here).