Penrose型镶嵌的对称性
Symmetry properties of Penrose type tilings
摘要：
彭罗斯镶嵌与某些十次准晶的原子结构直接相关，尽管它是非周期性的，但它是高度对称的。已知数字1、$-τ$、$(-τ)^2$、$(-τ)^3$、.、其中，$τ=(1+\sqrt{5})/2$是Penrose平铺的缩放因子。我们发现，一组的标度因子是更大的，对于他们中的大多数相应的暴胀中心的数量是无限的。
英文摘要：
The Penrose tiling is directly related to the atomic structure of certain decagonal quasicrystals and, despite its aperiodicity, is highly symmetric. It is known that the numbers 1, $-τ$, $(-τ)^2$, $(-τ)^3$, ..., where $τ=(1+\sqrt{5})/2$, are scaling factors of the Penrose tiling. We show that the set of scaling factors is much larger, and for most of them the number of the corresponding inflation centers is infinite.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
