Distinct band gaps and isotropy combined in icosahedral band gap materials

Icosahedral band gap materials (BGMs) optimally combine the distinct band gaps of periodic BGMs with the high rotational symmetry of quasiperiodic structures. This is shown experimentally for longitudinal and transverse polarized elastic waves in a phononic crystal based on the three-dimensional Penrose tiling (3D-PT) and applies equally to photonic crystals. The ability of icosahedral BGMs to form Bragg-type band gaps follows from the similarity between the 3D-PT and the face-centered cubic structure (its periodic average structure). The 3D quasiperiodic BGM lacks bands of strong transmission like random or disordered BGMs but shows clear band gaps like periodic BGMs do.