Rhombic dodecahedron

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 .

Rhombic icosahedron

A rhombic icosahedron (or rhombic icosacontahedron ) is a polyhedron shaped like an oblate sphere .

It is composed of 20 rhombic faces, where three, four, or five of which meet at each vertex. It has 10 faces on the polar axis with 10 rhombi following the equator.

Even though all the faces are congruent, the rhombic icosahedron is not face-transitive , since one may distinguish whether a particular face is near the equator or a pole by examining the types of vertices surrounding that face.

Rhombic triacontahedron

In geometry , the rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. It is an Archimedean dual solid, or a Catalan solid . It is the polyhedral dual of the icosidodecahedron , and it is a zonohedron .

The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio , φ, so that the acute angles on each face measure 2 tan ?1 (1/φ) = tan ?1 (2), or approximately 63.43°. A rhombus so obtained is called a golden rhombus .