I see nothing wrong with having the LED's on just one side of the cube. Which ones actually light would be dependent on the position of the accelerometer inside. Of course, you won't be able to see it, if the LED side is down. I don't see that as a problem for a school project, since you would know what the number should be for that position. A simple workaround would be to have the LED's on a pair of opposite sides.
Perhaps a tetrahedron might make an easier piece to work with.
Or, you could change the game a little...
Put the accelerometer in a ball (or any other shape, e.g. any Platonic solid). Transmit how it comes to rest to a stationary pad with the LEDs on it. That approach is a bit more complex because of the presumptive RF link, so it may be a bit much for just 3 weeks of work.
John