中文摘要：

研究十二次对称准晶体模型的几何结构性质.修正了Socolar在正方形-菱形-六边形拼图模型中自相似变换的错误.在Stampfli-Gahler正方形-菱形-三角形拼图模型的基础上,成功地构造出了准晶胞,使得十二次对称准周期结构可以用覆盖理论描述.

英文摘要：

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.