I have compiled all of the papers in the first 4 sections into an eBbook, called "A Geometric Analysis of the Five Platonic Solids and Other Semi-Regular Polyhedra (With an Introduction to the Phi Ratio)." The book contains over 140 diagrams, and is aimed at students, teachers, and the general reader. The book also contains comprehensive lookup tables, which the papers do not.
I can assure you that there is not another textbook out there that combines clear, simple explanations and mathematical rigor. The only knowledge required is high school algebra and elementary trigonometry. In the book, I avoid trigonometry unless calculating central and surface angles. If you can understand the Pythagorean Theorem, you can understand almost everything in this book.
Special thanks to Rick Parris for his excellent free software WinGeom, which was used to create the drawings in these pages.
WinGeom is available at http://math.exeter.edu/rparris/wingeom.html.
Can geometry be exciting? It can for those who can appreciate the beauty of numbers and their relationships.
This book contains a meticulous geometric investigation of the 5 Platonic Solids and 5 other important polyhedra, as well as reference charts for each solid. 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.
Also 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.
With over 140 illustrations, this book is perfect for teachers and students of geometry alike. It is a must for those who are serious about sacred geometry.
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.
Note: Requires knowledge of algebra and elementary trigonometry.
"I'm studying to become a carpenter and earlier this year I got a challenge to make an icosahedron from 10cm by 10cm by 10cm cube. Well, it didn't work out at all since I was totally clueless about the angles etc. I just couldn't figure them out by myself.
"After reading your articles I think I understand platonic solids a little better now. Very interesting stuff!
"Here's a few photos I'd like to share with you since you helped me so much. Without you I couldn't have constructed this."