This polyhedron compound contains one rhombic enneacontahedron (RE) and 30 icosahedra. Each icosahedron is merged with a thin rhombus so that the edges of the rhombus are on the adjacent faces of the icosahedron.

This assembly can be used to facilitate recalling certain geometrical facts, such as:

1. The rhombic enneacontahedron is bordered by 60 fat rhombi (with diagonal ratio equal to ) and 30 thin rhombi (with diagonal ratio equal to , where is the golden ratio).

2. The thin rhombi coincide with the faces of the rhombic triacontahedron.

3. The angle between two adjacent faces of the icosahedron equals the large angle of the thin rhombi, .

4. The edge length of a fat rhombi is , and from thin rhombi is . In general, . Notice that an integer is obtained when is even. In this sequence the ratio of two adjacent numbers converges to .