Version:            (using KDE 4.0.83)
Installed from:    SuSE RPMs

Kubrick currently allows you to set the length of each of the 3 dimension on the cube (or rather prism, if the lengths are not all the same).  This adds flexibility.  However, some people have found a way to extend the principles behind the Rubik's cubes to larger and smaller numbers of dimensions.  So far 2D, 4D, and 5D cubes have been developed, and in principle any number of dimensions above 2 is possible.  You can see the original 4D cube at the link below, and there are links to 2D and 5D implementations as well.  The link shows how such a cube can be made and has an example java program implementing the puzzle.  Solving the 4D puzzle is a lot of fun at least for me.

http://www.superliminal.com/cube/cube.htm

To put it simply, for the 3D Rubik's cube you have 6 square sides, each side divided into 9 (3x3) smaller squares.  The goal is to rotate sets of squares in 3 dimensions to get all of the square on one side to be the same color.  In the 4D case, you have 8 cubes (each equivalent to the sides in a 3D cube), each cube divided into 27 (3x3x3) smaller cubes.  The goal is to rotate the sets of cubes in 4 dimensions to get all the cubes on one "side" to be the same color.  It sounds confusing but once you get some practice it become surprisingly intuitive.  The 2D version (Rubik's square) uses 4 lines while the 5D version uses 10 4D hypercubes.  The mathematics behind the rotation of a 4D cube (a hypercube or tesseract) are well-established, there is even a standard linux screensaver to display them (and other 4D objects).  

More details regarding the mathematics behind it, including the number of pieces and number of combinations, can be found here:
http://www.gravitation3d.com/magiccube5d/anatomy.html

I think it would be great of Kubrick supported larger or smaller numbers of dimensions as well.  There shouldn't be a licensing problem, according to their website their license amounts to "please ask us first" and that is just for including the program in a commercial bundle, not the concept and not non-commercial bundles (I would ask anyway, of course).  The magic cube 4D program shows an efficient way to interact with the cube, or you could adapt the existing Kubrick interface for working in higher dimensions, or offer both.  I don't see any reason to make a 6D or higher cube, although you could if you want, and 5D may be pushing it, but 2D and 4D would definitely be fun.

1D would be a bit more difficult because there is no way to really scramble it.  However, a way to implement it would be to have a line divided into shorter segments of different colors.  By clicking on a line the segment above it and the segment below it switch places.  The goal would be to move the colors around so the order of the colors matches that of an target line shown next to your line.  So for instance if you had Red-Green-Blue-Yellow, and the target is Blue-Green-Red-Yellow, you would click on the green which would switch the places of the red and blue and thus your line would match the target.  Actually, just in general making it so you have to match some arbitrary target arrangement of colors instead of making them all the same might actually be an interesting variation on the normal Rubik's cube idea no matter how many dimensions you are working with.