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.
