Quasiperiodic Tilings Derived from Deformed Cuboctahedra

摘要

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.