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

.