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，并已得到广泛研究。特别是，由六边形（$H$）、船形（$B$）和星形（$S$）构成的图案很快被展示出来，许多物理学家发表了关于后来被称为 $HBS$ 铺砌的研究，但尚无文章或专著系统整合其全部已知成果。本文首先完成了此项综述工作，继而引入新的装饰图案与性质，包括显式替换规则。对于后者，星形存在三种变体，因此在我们称为星形砖块组的集合中共有 5 种原型砖块。然而该集合恰好能生成严格的 $HBS$ 铺砌——这些铺砌使用 3 种砖块，并采用常规装饰（箭头）或例如阿曼条形标记进行装饰。本文还提出了另一种称为宝石砖块组的新砖块集合，该集合衍生自星形砖块组。