Tilings, coverings, clusters and quasicrystals

A quasiperiodic covering of the plane by regular decagons and an analogous structure in three dimensions are described. The 3D pattern consists of interpenetrating triacontahedral clusters, related to the $tt^{\mathrn{3}}$ inflation rule for the 3D Penrose tiling patterns. The overlap regions are triacontahedron faces, rhombic dodecahedra and rhombic icosahedra, The structure leads to a plausible model for the T2 icosahedral quasicrystalline phases