用三个多边形平铺是不可判定的

arXiv - MATH - Metric Geometry Pub Date : 2024-09-17 DOI:arxiv-2409.11582

Erik D. Demaine, Stefan Langerman

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摘要

我们证明了下面的问题是共RE完成的，因此是不可判定的：给定三个简单多边形，是否存在一个平面平铺，其中每个平铺都是三个多边形之一的等值体（允许或禁止反射）？这一结果改进了之前需要五个多边形的最佳构造。

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Tiling with Three Polygons is Undecidable

We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of the three polygons (either allowing or forbidding reflections)? This result improves on the best previous construction which requires five polygons.

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arXiv - MATH - Metric Geometry

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