I have been doing some theoretical thinking about the 4th dimension, and even got my entire guitar 4 class in school to think about it, half stoned. We confused the stuff out of the Orchestra kids, we use their room because Guitar is too cool to need its own room. We talked about the Hypercube (4D cube), 4D spheres, and 4D pyramids. Later that day, I had an epiphany-a 4th dimensional Rubik's cube. I first drew out the hypercube, then segmented it proportionally to create what would be the 4D Rubik's cube. That was the easy part, the hard part was figuring out how it moved. I finally figured it out, then looked on the internets to see if anyone else had the same idea. Turns out they did, and here is the link to a 4D Rubik's cube simulator, that's simulator, it can't actually create the fourth dimension because we are creatures of the third dimension viewing a deformed 3D object on a 2D screen.
http://www.superliminal.com/cube/cube.htmClick on the picture at the top of the webpage to go to a simple applet for demonstrations.