It can also be seen as a nonuniform truncated icosahedron with pyramids augmented to the pentagonal and hexagonal faces with heights adjusted until the dihedral angles are zero, and the two pyramid type side edges are equal length.

This construction is expressed in the Conway polyhedron notation jtI with join operator j.

Without the equal edge constraint, the wide rhombi are kites if limited only by the icosahedral symmetry.

It is also called a rhombic enenicontahedron in Lloyd Kahn's Domebook 2.

Since the rhombic enneacontahedron is contained in a rhombic dodecahedron whose inscribed sphere is identical to its own inscribed sphere, the value of the optimal packing fraction is a corollary of the Kepler conjecture: it can be achieved by putting a rhombicuboctahedron in each cell of the rhombic dodecahedral honeycomb, and it cannot be surpassed, since otherwise the optimal packing density of spheres could be surpassed by putting a sphere in each rhombicuboctahedron of the hypothetical packing which surpasses it.