Hexagonal quasiperiodic tilings as decorations of periodic lattices

Symmetry sharing facilitates coherent interfaces which can transition from periodic to quasiperiodic structures. Motivated by the design and construction of such systems, we present hexagonal quasiperiodic tilings with a single edge-length which can be considered as decorations of a periodic lattice. We introduce these tilings by modifying an existing family of golden-mean trigonal and hexagonal tilings, and discuss their properties in terms of this wider family. Then, we show how the vertices of these new systems can be considered as decorations or sublattice sets of a periodic triangular lattice. We conclude by simulating a simple Ising model on one of these decorations, and compare this system to a triangular lattice with random defects.