Hexagon-boat-star (HBS) pentagonal tilings often appear in the description of decagonal quasicrystals and their periodic approximants. Being related to the Penrose tiling, they differ from the latter by a significantly higher packing density of vertices, which, in turn, depends on the relative frequency of appearance of the H, B and S tiles. Since boats (also known as “ivy leaves”) have the lowest packing density, reducing their number in the tiling leads to an increase in its packing density. The paper proposes an inflation rule for a chiral tiling, which, in principle, contains no boats and therefore has the highest possible density among HBS tilings. The relationship between the tiling and the real structures of crystal approximants of decagonal quasicrystals is discussed.

中文翻译：

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星形和六边形的手性五边形准周期平铺的膨胀规则


六边形船星 （HBS） 五边形平铺经常出现在十边形准晶体及其周期性近似值的描述中。由于与 Penrose 平铺相关，它们与后者的不同之处在于顶点的打包密度明显更高，这反过来又取决于 H、B 和 S 平铺的相对出现频率。由于船（也称为“常春藤叶”）的堆积密度最低，因此减少它们在平铺中的数量会导致其堆积密度增加。本文提出了手性平铺的膨胀规则，原则上不包含船，因此在 HBS 平铺中具有最高的密度。讨论了平铺与十边形准晶体的晶体近似物的实际结构之间的关系。