A Sequence of Inscribed Platonic Solids
This Demonstration shows a particular sequence of inscribed Platonic solids.
This combination was designed by J. H. Conway and is sold by Zometool as Kepler's Kosmos (although it may not be what Kepler had in mind).
 W. W. R. Ball and H. M. S. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover, 1987 pp. 133, 160.
 Zometool. "Kepler's Kosmos." (Sept 19, 2013) zometool.com/products/detail/keplers-kosmos.