Introduction

Introduction

Several years ago John R. Hendricks introduced a coordinated set of definitions for magic cubes. It included a new definition for the ‘perfect’ magic cube, which is applicable for magic hypercubes of any dimension.

This inspired me to investigate the different definitions of ‘perfect’ magic cubes that had appeared over the years. The result was a new page that discussed the subject. However, I ended up with more questions then when I started, so developed a series of spreadsheets to investigate many characteristics of magic cubes.

After looking closely at over 200 published magic cubes of order 3 to 17, I am amazed at how few cubes I found that had all identical features. Considering the large number of possible combinations available to form a magic cube of a given order, it is not surprising I found very few duplicate cubes. However, features such as number, type, and location of included magic squares, feature variations in the oblique squares, etc., were found to be extremely varied.
The result is this new series of pages, which explores the subject in some depth. With one or two possible exceptions, all magic cubes shown on these pages will have different features (or at least will be different orders).

As is usual with the other pages on this site, I intend to keep the discussions simple and will not normally go into methods of construction. Methods, and involved mathematics, will be left to others that are more qualified to present them. These pages will be more concerned with basic principles and a survey of the history and variety of magic cubes.