Eight different decagonal tilings derived from rhombic Penrose tiling

Abstract

We found 32 variations of dot tiling (DT) reported previously [J. Alloy. Comp. 342 (2002) p.206], which is similar to a tiling consisting of pentagon, hexagons, nonagon and decagons (PHND) [Phil. Mag. A l76 (1997) p.85] employed in the structure analysis of decagonal quasicrystals. They are its superstructures, with a five times larger unit cell in four-dimensional space. These tilings are built up by adding one dot in each fat rhombus in the rhombic Penrose tiling. Eight tilings among 32 DTs do not break the local symmetries of the eight types of vertices in the rhombic Penrose tiling. The eight tilings and their occupation domains are shown.

Keywords:

• electron theory
• quasicrystalline alloys
• quasicrystals