Self-similar transformation and quasi-unit cell construction of quasi-periodic structure with twelve-fold rotational symmetry

Abstract

The structural properties of a quasicrystal model with twelve-fold rotational symmetry are studied. We correct the errors in the self-similar transformation of the square-rhombus-hexagon tiling model proposed by Socolar. Based on the Stampfli-Ghler square-rhombus-triangle tiling model， the quasi-unit cell is successfully constructed， which can describe the dodecagonal quasiperiodic structure by the covering theory.