Fang Fang, Klee Irwin (2016)

The construction of an icosahedral quasicrystal and a quasicrystalline spin network are obtained by spacing the parallel planes in an icosagrid with the Fibonacci sequence. This quasicrystal can also be thought of as a golden composition of five sets of Fibonacci tetragrids. We found that this quasicrystal embeds the quasicrystals that are golden compositions of the three-dimensional tetrahedral cross-sections of the Elser-Sloane quasicrystal, which is a four-dimensional cut-and-project of the E8 lattice. These compound quasicrystals are subsets of the quasicrystalline spin network, and the former can be enriched to form the latter. This creates a mapping between the quasicrystalline spin network and the E8 lattice.