A QUASIPERIODIC PATTERN GENERATED BY MIXING DODECAHEDRAL AND ICOSAHEDRAL LATTICE. T. Soma, Department of Mathematics and Computing Science The University of the South Pacific, Suva, Fiji, Y. Watanabe, The Institute of Physical and Chemical Research Wako-shi, Saitama 351-01 Japan

A 16 by 16 projection matrix is presented which produces basis vectors in pattern space as a combination or mixing of vectors from the center to vertices of a pentagonal dodecahedron and an icosahedron. The two polyhedrons are arranged such that the vectors of an icosahedron coincide with five-fold symmetry axes, and those of a dodecahedron with three-fold symmetry axes of an icosidodecahedron. The mixing ratio, the ratio of the length of basis vectors for an icosahedron to that for a dodecahedron can take any positive value and the 16-D unit cube projected to pattern space is an enneacontrahedron truncated by a triacontrahedron. The depth of truncation changes as the mixing ratio and for 1 to 1 mixing an equilateral truncated rhombic enneacontrahedron is obtained. Quasiperiodic patterns or tilings by the projection method using the 16 by 16 matrix are presented.