High Quality Content by WIKIPEDIA articles! In geometry, the rhombic dodecahedron is a convex polyhedron with 12 rhombic faces. It is an Archimedean dual solid, or a Catalan solid. Its dual is the cuboctahedron. It is the polyhedral dual of the cuboctahedron, and a zonohedron. The long diagonal of each face is exactly 2 times the length of the short diagonal, so that the acute angles on each face measure cos–1(1/3), or approximately 70.53°. Being the dual of an Archimedean polyhedron, the rhombic dodecahedron is face-transitive, meaning the symmetry group of the solid acts transitively on the set of faces. In elementary terms, this means that for any two faces A and B there is a rotation or reflection of the solid that leaves it occupying the same region of space while moving face A to face B.

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