Consider the egdes of a generic 3x3x3 cube: they can be all different or all the same, they can be orientable or they can have just one orientation. Consider now the corners: they can be all different or all the same, they can be orientable or they can have just one orientation. Finally consider the centers: if you dont want to get the center caps off the centers cannot be permuted, but they can have 1, 2, or 4 orientations. This gives: 2 possibilities (equal or different edges) times 2 possibilities (orientable or non-orientable edges) times 2 possibilities (equal or different corners) times 2 possibilities (orientable or non-orientable corners) times 3 possibilities (centers with 1,2,4 orientations) for a total of 48 categories of cubes. I've designed cubes for each of these 48 categories. #cubes #orientation #permutations #Rubik