The dualisation method revisited : dualisation of product Laguerre complexes as a unifying framework

Abstract

A general framework based on the dualisation of Laguerre cell complexes is presented, which allows to construct and understand a large variety of quasiperiodic tilings, both new ones and well known old ones. The general framework is illustrated with many examples, which are all based on cell complexes which are products of 2-dimensional complexes. The simple structure of these examples makes it particularly easy to understand how the general procedure works. Yet the examples are sufficiently versatile to exploit the power and flexibility of the method.