Dissection of Bilunabirotunda into Two Pentagonal Dipyramids and a Rhombic Dodecahedron of the Second Kind

This Demonstration shows a dissection of a bilunabirotunda into two pentagonal dipyramids and a rhombic dodecahedron of the second kind. The faces of the dipyramids are halves of the golden rhombus.

Since the rhombic dodecahedron of the second kind can be decomposed into two oblate and two prolate rhombohedra, five rhombic dodecahedra can be dissected into a triacontahedron. The triacontahedron can be decomposed into a dodecahedron and 12 pyramids. So three bilunabirotundas and the dodecahedron can be decomposed into the triacontahedron and three rhombic dodecahedra of the second kind or into eight rhombic dodecahedra of the second kind.