Cluster of 45 Polyhedra around a Rhombic Hexacontahedron
Rhombic triacontahedra (RT) and rhombic hexecontahedra (RH) are layered to form a structure similar to one sometimes found in quasicrystals. The total number of polyhedra can be enumerated as follows: 1 RH + 12 RT + 20 RT + 12 RH = 45.
 S. Kabai, S. Bérczi, and L. Szilassi, "Clusters Produced by Placing Rhombic Triacontahedra at the Vertices of Polyhedra," The Mathematica Journal, 14, Sep 2012. www.mathematica-journal.com/2012/09/clusters-produced-by-placing-rhombic-triacontahedra-at-the-vertices-of-polyhedra.
"Cluster of 45 Polyhedra around a Rhombic Hexacontahedron"
Wolfram Demonstrations Project
Published: October 26 2015