Dissection of Two Rhombic Solids into an Icosidodecahedron and a Rhomb-Icosi-Dodecahedron
This Demonstration gives a dissection of the rhombic hexecontahedron and of a rhombic-like solid that consists of 30 halves of the rhombic dodecahedron of the second kind put on a triacontahedron; the result is a combination of the icosidodecahedron and the rhomb-icosi-dodecahedron.
That such dissections exist follows from [1], where it is shown that certain combinations of Platonic and Archimedean solids have Dehn invariant 0.
[1] J. H. Conway, C. Radin, and L. Sadun, "On Angles Whose Squared Trigonometric Functions Are Rational," Discrete & Computational Geometry, 22(3), 1999 pp. 321–332.
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