This page, which is mostly about the oh-so-trendy Golden Ratio (boooooring!!) has a neat animation showing how a dodecahedron (A.K.A. "twelve-sided-dice") may be hinged and transformed into a cube in one smooth motion. Euclid showed that a dodecahedron is related to a cube, and could be constructed by putting "roofs" in each of the faces of the cube.
(The page has a better, bigger animation.)