The Handbook of Cubic Math unveils the theory involved in Rubik's Cube's solution, the potential applications of that theory to other similar puzzles, and how the cube provides a physical example for many concepts in mathematics where such examples are difficult to find.

The authors have been able to cover and explain these topics in a way which is easily understandable to the layman, suitable for a junior-high-school or high-school course in math, and appropriate for a college course in modern algebra.

This manual will satisfy the experts' curiosity about the moves that lead to the solution of the cube and will offer a useful supplementary teaching aid to the beginners.

Preface

1. Introduction
2. A Cubik Orientation
3. Restoring the Cube
4. The What, Why, and How of Cube Movements
5. Improved Restoration Processes
6. The Cube Group and Subgroups
7. Permutation Structures and the Order of Groups
8. Advanced Restoration Methods
9. Epilogue

A. A Small Catalogue of Processes
B. Solutions to Exercises
Index

   Preface » (PDF, 33 KB)
   Chapter 2: A Cubik Orientation » (PDF, 84 KB)

David Singmaster is the top world authority on the mathematics of Rubik's Cube. He originated the notation system that is used throughout the world to communicate about the cube.

Alexander H. Frey Jr has a PhD in mathematics from the University of Washington and was a computer architect with IBM. He is now retired.

"The best book yet written – or likely to be written – on the wonders and the dark, unsolved misteries of the cube"
Martin Gardiner

"Frey and Singmaster give a nicely blended discussion of specific algorithms for the cube together with some underlying theoretical concepts from group theory. Thus, cubists will be able to cure their insomnia by reading Chapter 3, and then perhaps satisfy their aroused curiosity about what is really going on by reading further"
David M. Goldschmidt, Professor of Mathematics, University of California, Berkeley

"Frey and Singmaster masterfully use the Rubik's cube to give a very tangible and tactile feel to the abstract concept of a group ... the book remains the definitive source for cube mathematics and presents an interesting and accessible introduction to group theory."
David A. Reimann, in Mathematical Reviews, Issue 2012d