Many people are familiar with the Rubik’s Cube, the 3x3x3 cube with colored faces that can be moved out of position and then, ideally, twisted back into place. This toy, originally called the Magic Cube, was invented by Ernő Rubik in 1974 while he was a lecturer at the Academy of Applied Arts and Crafts in Budapest, Hungary. In 1980 the cube made its way to other countries and spawned, among other things, a one-season cartoon series Rubik, the Amazing Cube in which some kids use a magical come-to-life Rubik’s Cube to solve mysteries, while avoiding the mandatory evil magician who wants to steal the Cube.
There is a lot more information on the official Rubik’s Cube website, including the fact that the world record for speed in solving the cube is only 16.5 seconds. The latest Rubik’s news was an announcement in May 2007 that Gene Cooperman (a professor) and Dan Kunkle (a graduate student) at Northeastern University proved that no matter how mixed up the cube, it can be solved in at most 26 moves. [This is an improvement from 27 moves, a record that stood for 10 years; the least upper bound may be in the low 20s.]
What about the hypercube? The hypercube is a four-dimentional object in which each of the “faces” is actually a cube (much the same way that in a three-dimensional cube each face is a square, and in a two-dimensional square each face is a line). There are a plethora of mathematical features of the hypercube: for example, a line has 2 vertices, a square has 4, a cube has 8, and the hypercube has 16, illustrating the fact that an n-dimensional “square” has 2n vertices.
A Rubik’s Hypercube would be a four-dimensional object in which each face, instead of being a square, is a Rubik’s Cube. Does such a thing exist? Not in real life (the whole dimension thing makes a 4D object difficult to build) but on the Internet all things are possible. Yes, Don Hatch, Melinda Green, and Jay Berkenbilt created/maintain a Magic Cube 4D Applet. But it doesn’t stop there! Roice Nelson “[i]n the spirit of taking things too far” created MagicCube5D in which each face is a Rubik’s Hypercube. And if that doesn’t satisfy you, you can join the 4D Cubing Group on Yahoo (which, in the 7 days before this post, had 2 new members and 5 new messages).
The idea for this Juxtaposition came from Peter Baéz while he was researching the hypercube for a class.