一个五边形晶体，黄金分割，壁龛包装和非周期性瓷砖
A Pentagonal Crystal, the Golden Section, alcove packing and aperiodic tilings
摘要：
基于长度比等于黄金分割的等腰三角形，对非周期彭罗斯镶嵌中出现的五重对称图案给出了李理论解释.具体地，基于柏原的晶体构建了表现出这种五重对称性的$B(\infty)$晶体。结果表明，它可以表示为$A_4$型的柏原$B(\infty)$晶体。具有$(2n+1)$折叠对称性的类似晶体被表示为$A_{2n}$型的柏原晶体。后者的重量图激发了更高的非周期性平铺。在另一种方法中，可以看到壁龛填充给出$A_4$类型的非周期性平铺。最后，$2m$折叠对称性与$B_m$型有关.
英文摘要：
A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a $B(\infty)$ crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara $B(\infty)$ crystal in type $A_4$. Similar crystals with $(2n+1)$-fold symmetry are represented as Kashiwara crystals in type $A_{2n}$. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $A_4$. Finally $2m$-fold symmetry is related to type $B_m$.
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。
