Symmetric Compositions of Rhombic Dodecahedra of the Second Kind

This Demonstration shows some symmetric compositions of rhombic dodecahedra of the second kind.

It also shows that a rhombic dodecahedron of the second kind consists of two prolate and two oblate golden rhombohedra. The ratio of the diagonals is the golden ratio , and the same is true for the ratio of the volumes of the rhombohedra. The area of the rhombus is . The volume of the dodecahedron is .