A quasi-lattice based on a cuboctahedron. 1. Projection method
Yasunori Watanabe, Takashi Soma, Masatoshi Ito · Crystallography Reports · 2004
A three-dimensional (3D) quasi-lattice ( QL ) based on a cuboctahedron is obtained by the projection from a seven-dimensional hypercubic base lattice space to a 3D tile-space. The projection is defined by a lattice matrix that consists of two projection matrices from the base lattice space to a tile-space and perp-space, respectively. In selecting points in the test window, the method of infinitesimal transfer of the test window is used and the boundary conditions of the test window are investigated. The QL obtained is composed of four kinds of prototiles, which are derived by choosing triplets out of seven basis vectors in the tile-space. The QL contains three kinds of dodecahedral clusters, which play an important role as packing units in the structure. A modification of the lattice matrix making the QL periodic in the z direction is also considered.