Rhombic Compound

A beautiful composition of a rhombic dodecahedron and a rhombic triacontahedron based on the sculpture Dos Mons by Josep Rey Nadal.

Proof that the edges of the rhombic dodecahedron are coplanar to the faces of the rhombic triacontahedron:

Let:

• Yellow = (1, 1, 1)

• Red = (0, 0, 2)

• Blue = (1, 0, φ)

• Green = (0, 1/φ, φ)

Then, the point (2-φ, 2-φ, φ) belongs to the edges:

• Yellow · λ + Red · (1-λ) = (λ, λ, 2-λ)

• Blue · λ + Green · (1-λ) = (λ, (1-λ)/φ, φ)

for the same value of λ = 2-φ