PROJECTION METHOD FOR 4D NONORTHOGONAL HYPERLATTICES

The Wigner-Seitz cell of a lattice in n-dimensional space displays the complete point group of such a lattice. The vertices of the cell when projected onto pseudo space can serve as the outer shape of acceptanc e domain or motif. This general procedure leads to acceptance domain o r motif identical to those discussed in literature for primitive ortho gonal hyperlattices. Example of 4d non-orthogonal hyperlattices corres ponding to 12-fold symmetry will be considered. It will be shown that the first Wigner-Seitz cell degenerates into more than one shape in 2d pseudo space and can serve as a natural partition of the motif. Follo wing a parallel procedure, the consequence of projection of first 4d B rillouin zone will also be discussed.