圆锥体和凸多面体的重叠展开
Overlapping Unfoldings of Cones and Convex Polyhedra
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中文总结 AI 辅助
研究丢勒问题时反转目标，找到能在某点重叠到任意给定厚度的凸多面体展开。主要成果为：允许非沿边缘切割时，存在可任意厚度重叠展开的凸多面体；对任意厚度，存在边缘展开能重叠到该厚度的凸多面体。
中文摘要 AI 辅助
对丢勒问题的研究聚焦于避免重叠的凸多面体的边缘展开。我们反转目标，找到在某点重叠到任意给定厚度t的展开。我们有两个主要结果。其一，如果允许不沿多面体边缘的展开切割，那么存在一个能以任意给定厚度重叠展开的凸多面体。其二，对于任意给定厚度，存在一个边缘展开能重叠到该厚度的凸多面体。
英文摘要
Research on Dürer's problem focuses on edge unfoldings of convex polyhedra that avoid overlap. We invert the goal and find unfoldings that overlap at some point to any given thickness t. We have two main results. The first is that, if we allow unfolding cuts that do not follow polyhedron edges, then there is a convex polyhedron that can unfold with overlap of any given thickness. The second result is that for any given thickness, there is a convex polyhedron with an edge unfolding that overlaps to that thickness.
