Rubik Tesseract Paper

Please click here for a downloadable copy of the Kamack-Keane paper.

Many will recall that Rubik's Cube had its heyday from 1980 to about 1983. During 1981, H. J. Kamack and T. R. Keane developed a mathematical model of a 4-dimensional analogue, which is described in this paper. An early version of the paper was sent to Douglas Hofstadter, who discussed the work in his column Metamagical Themas in the July 1982 issue of Scientific American.

As a result, Kamack and Keane received a great deal of mail requesting copies of the manuscript and, over time, several hundred copies were sent out. The paper was never published, but there have been several references to the work posted on the Internet. The paper has been the basis for several computer simulations in which a Rubik tesseract can be scrambled and unscrambled on the screen in a manner similar to manipulation of a physical Rubik cube. [There is an excellent website maintained by Georges Helm which makes reference to all sorts of cube puzzles and their variants].

This PDF version of the paper was created in 2005. It is intended to be, insofar as possible, an exact copy of the June 1982 version of the manuscript. Much has happened since 1982; for example, the computer language used in the original paper is no longer used. Nevertheless, it is thought to be appropriate to post this version for historic reasons.

This page updated May 25, 2013