A Sequence of Inscribed Platonic Solids

This Demonstration shows a particular sequence of inscribed Platonic solids.

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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).
References
[1] W. W. R. Ball and H. M. S. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover, 1987 pp. 133, 160.
[2] Zometool. "Kepler's Kosmos." (Sept 19, 2013) zometool.com/products/detail/keplers-kosmos.
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