作为旋转对称等面体拼接基本域的多角形和多角形
Polyominoes and Polyiamonds as Fundamental Domains of Isohedral Tilings with Rotational Symmetry
摘要：
我们描述了计算机算法，产生的n-omino或n-iamond瓷砖，其中的瓷砖是基本域和瓷砖有3，4，或6倍旋转对称的一套完整的等面体平铺。这种镶嵌的对称群是p3、p31 m、p4、p4 g和p6类型。不存在对称群为p3 m1、p4 m或p6 m的以多角形或多面体为基本域的等面体镶嵌。我们显示算法的输出，并给出枚举表的小值n。这扩展了我们早期的工作（Fukuda et al 2006，2008）。
英文摘要：
We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are of types p3, p31m, p4, p4g, and p6. There are no isohedral tilings with symmetry groups p3m1, p4m, or p6m that have polyominoes or polyiamonds as fundamental domains. We display the algorithms' output and give enumeration tables for small values of n. This expands on our earlier works (Fukuda et al 2006, 2008).
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