This polyhedron has twelve identical intersecting pentagonal planes. The twelve vertices are also identical. The surface is one of two first described by Johannes Kepler in 1619, and now known as a Kepler-Poinsot solid.
Compare models MA.304722.027, MA.304722.174, MA.304722.499, MA.304722.653, and 1979.0102.230.
References:
H. M. Cundy and A. P. Rollet, Mathematical Models, Oxford: The Clarendon Press, 1961.
Magnus J. Wenninger, Polyhedron Models, Cambridge: The University Press, 1971, p. 39.
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