A rhombic icosahedron (or rhombic icosacontahedron) is a polyhedron shaped like an oblate sphere.
It is composed of 20 rhombic faces, of which three, four, or five 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.
The rhombic icosahedron is a zonohedron that is dual to an irregular-faced pentagonal gyrobicupola.
It has D5d symmetry.