Why a cube? Is there some reason to use six sides as opposed to a tetrahedron or octohedron? Or was it just convenient/convention because of the popularity of cubes.
I think a cube is preferred to octahedron because of efficiency/performance related reasons. I don't know why it's preferred over a tetrahedron but it might be due to the same distortion problems that arise when using a sphere map. I'm not sure about that last bit though.