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，许多物理学家随后发表了关于他们后来称为 HBS 铺砌的研究，但尚无文章或书籍全面整合我们对此的所有认知。本文首先完成了这项工作，继而引入包括显式替换在内的新装饰与性质。对于后者，星形存在三种变体，因此在我们称为星形砖块集的集合中总共有 5 种原型砖块。然而，该集合恰好生成严格的 HBS 铺砌，这些铺砌使用 3 种砖块并饰以常规装饰（箭头）或例如 Ammann 条标记等。本文还提出了另一个称为宝石集的新砖块集，其衍生自星形砖块集。