The existence of such a decomposition follows from [2] or from the Demonstration referenced in the Related Links and [1]. This dissection as well as the dissection of a dodecahedron into eight parts (if original) could be made into a commercial puzzle.

[1] V. G. Boltyanskii, Tretja Problema Hilberta, Moscow: Nauka, 1977. Translated by R. A. Silverman as Hilbert's Third Problem (New York: John Wiley & Sons, Inc., 1978). [2] I. Hafner, "Decomposition of Three Bilunabirotundas and Dodecahedron to Rhombic Solids," Visual Mathematics, 9(2), 2007 article 6.