PERIODIC AND QUASI-PERIODIC LAGUERRE TILINGS

Abstract

The Laguerre construction extends and unifies the notions of Voronoi (or Dirichlet) and Delaunay complex. It is shown how the standard projection formalism for the generation of quasi-periodic tilings from higher-dimensional periodic “oblique” (or “klotz”) tilings associated to periodic Voronoi and Delaunay complexes also applies more generally to Laguerre complexes. It turns out that all quasi-periodic tilings obtained this way are Laguerre tilings themselves.