Generalized Rauzy tilings: construction and electronic properties

We study a new class of quasiperiodic codimension one tilings based on a natural generalization of the Fibonacci chain. These so-called generalized Rauzy tilings allow for simple and explicit expressions of the site coordinates, and their associated tight-binding Hamiltonians are quickly written as band (Toeplitz-like) matrices. First results are given for their electronic properties which display similar behaviors as higher codimension tilings.