Quasiperiodic Tilings Derived from Deformed Cuboctahedra

Takashi Soma¹ and Yasunari Watanabe²*

¹3-32-2-109 Akatsuka-shinmachi, Itabashi-ku, Tokyo 175-0093, Japan
²Department of Information Systems, Teikyo Heisei University, 2289 Uruido, Ichihara, Chiba 290-0193, Japan
*E-mail address: watanabe@thu.ac.jp

(Received February 9, 2004; Accepted July 22, 2004)

Keywords: Quasiperiodic Tiling, Projection Method, Cuboctahedron

Abstract. 3D quasiperiodic tilings derived from deformed cuboctahedra are obtained by projection from 7D or 6D lattice space to 3D tile-space. Lattice matrices defining the projections from 7D or 6D lattice space to tile- and test-space are given by introducing a deformation parameter. Two types of lattice matrices are considered, orthonormal and row-wise orthogonal, both are corresponding to deformation of a cuboctahedron along the z-direction but the latter is corresponding to uniform deformation. Both 3D and 2D tilings are investigated though the latter is merely derived as a degenerate case of the former.