The rhombic icosahedron is a polyhedron shaped like an oblate sphere.

It has 5 faces (green on top figure) meeting at each of its 2 poles; these 2 vertices lie on its axis of 5-fold symmetry, which is perpendicular to 5 axes of 2-fold symmetry through the midpoints of opposite equatorial edges (example on top figure: most left-hand and most right-hand mid-edges).

The rhombic icosahedron has 5 sets of 8 parallel edges, described as 85 belts.

(*) (For example, on the left-hand figure): The orthogonal projection of the (vertical) belt of 10 middle faces of the rhombic triacontahedron is just the (horizontal) exterior regular decagon of the common orthogonal projection.

Removal of a further belt of 8 faces with parallel edges from the icosahedron results in the Bilinski dodecahedron, which is topologically equivalent but not congruent to the regular rhombic dodecahedron.