Structure Transition of the Three-Dimensional Penrose TilingUnder Phason Strain Field

Possible periodic structures resulting from three-dimensional Penrose tiling (3DPT) by introducing the so-called phason strain are studied. Only two types of cubic structures, simple cubic (sc) and body centered cubic (bcc), are possible. Numbers of the unit-cells, which are the same as those of the 3DPT, within each structure matrix of the sc/bcc structure are also given.