Quasiperiodic Tilings Derived from Deformed Cuboctahedra

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. 1