Rubik’s 4-Cube »
NBRubik’s cube has a natural extension to four-dimensional space. This article constructs the basic concepts of the puzzle and implements it in a program. The well-known three-dimensional Rubik’s cube 
consists of 27 unit subcubes. Each face 
of 
determines a set 
of nine subcubes that have a face in the same plane as 
. The set 
can be rotated around the normal through the center of 
. Rubik’s 4-cube (or 4D hypercube) 
consists of 81 unit 4-subcubes, each containing eight 3D subcubes. Each 3-face 
of 
determines a set 
of 27 4-subcubes that have a cube in the same hyperplane as 
. The set 
can be rotated around the normal (a plane) through the center of 
. Projecting the whole 4D configuration to 3D exhibits Rubik’s 4-cube as a four-dimensional extension of Rubik’s cube. Starting from a random coloring of the 4-cube, the goal of the puzzle is to return to the initial coloring of the 3-faces. Read More »
