Penrose-like tilings from projection of affine A 4 to affine H 2

Abstract

Abstract The present work offers a different perspective for the 5-fold symmetric quasicrystallography by employing affine H 2 as a subgroup of affine A 4. It is shown that the projection of the Voronoi cell of the root lattice A 4 can be dissociated as identical five decagons up to a rotation tiled by thick and thin rhombuses. Projection of the Voronoi cell of the weight lattice onto the Coxeter plane tessellates the plane with four different tiles: thick and thin rhombuses with different edge lengths and two types of hexagons. Structure of the local dihedral symmetry H 2 fixing a particular point on the Coxeter plane is determined.