Penrose tilings are the most famous aperiodic tilings, and they have been studied extensively. In particular, patterns composed with hexagons ($H$), boats ($B$) and stars ($S$) were soon exhibited and many physicists published on what they later called $HBS$ tilings, but no article or book combines all we know about them. This work is done here, before introducing new decorations and properties including explicit substitutions. For the latter, the star comes in three versions so we have 5 prototiles in what we call the Star tileset. Yet this set yields exactly the strict $HBS$ tilings formed using 3 tiles decorated with either the usual decorations (arrows) or Ammann bar markings for instance. Another new tileset called Gemstones is also presented, derived from the Star tileset.

翻译：彭罗斯铺砌是最著名的非周期铺砌，且已被广泛研究。特别是由六边形（$H$）、船形（$B$）和星形（$S$）构成的图案很快被揭示，许多物理学家后来发表了关于所谓$HBS$铺砌的论文，但尚无文章或书籍综合我们已知的所有内容。本文完成了这一工作，并引入了新的装饰与性质，包括显式替换规则。对于后者，星形具有三种变体，因此我们在所谓的星形瓦片集中共有5种原型瓦片。然而，该瓦片集恰好生成了严格的$HBS$铺砌，这些铺砌由3种瓦片组成，并配有常规装饰（箭头）或例如Ammann条形标记。本文还从星形瓦片集推导出另一个新瓦片集，称为宝石瓦片集。