论文标题
一个三瓷砖6倍金均值的瓷砖
A three tile 6-fold golden-mean tiling
论文作者
论文摘要
我们提出了一个多重长度的大型瓷砖，表现出6倍 - 旋转对称性。平铺的边缘长度与1：$τ$成比例，其中$τ$是金表示$ \ frac {1+ \ sqrt {5}}} {2} $。我们展示了如何使用简单的替代规则为其三个组成瓷砖生成平铺，然后我们用它们来证明瓷砖顶点的两部分性质。因此，我们表明，$ 1/[2τ^2] $的相对较大的Sublattice不平衡。同样，我们定义允许的顶点配置，然后再分析4维超空间的瓷砖结构。
We present a multi-edge-length aperiodic tiling which exhibits 6--fold rotational symmetry. The edge lengths of the tiling are proportional to 1:$τ$, where $τ$ is the golden mean $\frac{1+\sqrt{5}}{2}$. We show how the tiling can be generated using simple substitution rules for its three constituent tiles, which we then use to demonstrate the bipartite nature of the tiling vertices. As such, we show that there is a relatively large sublattice imbalance of $1/[2τ^2]$. Similarly, we define allowed vertex configurations before analysing the tiling structure in 4-dimensional hyperspace.
