An Essentially-three-dimensional Quasicrystal


Tohru Ogawa




As the generator of an essentially-3-D quasicrystal, some detail of a 3-D Penrose transformation is given. The expansion rate t3=4.236 is by far the larger than ever believed value t=1.618. The features of this model agree rather well with those of high-resolution electron micrograph. The Penrose logic of hierarchic generation of patterns is summarized and a new expression is also given for 2-D Penrose transformation.