Cut-and-project tilings constructed from crystallographic tilings

Abstract

An important method to construct aperiodic tilings is the method of canonical projection from higher dimensional lattices. Lattices are the orbits of special type of crystallographic groups. For example, Penrose tilings can be obtained from a lattice tiling of E5, by the cut-and project method. Developing a mathematical theory of crystallographic tilings and generalising the method of canonical projection to other crystallographic groups than lattices. Using this method one can hope to construct (interesting), completely new types of aperiodic tilings.