MIT CompGeom Group, Hugo A. Akitaya, Erik D. Demaine, Adam Hesterberg, Anna Lubiw, Jayson Lynch, Joseph O'Rourke, Frederick Stock, Josef Tkadlec
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引用次数: 0
摘要
多面体是由单位等边三角形组成的多边形，广义正三角形是每个面都是凸多面体的凸多面体。我们研究的是其中一个面可能是例外的变体。对于凸多边形 P，如果有一个凸多面体以 P 为一个面，而其他所有面都是凸多面体，那么我们就说 P 可以是圆顶的。我们的主要结果是完整地描述了哪些等角 n 边形可以被穹顶化：只有当 n 在 {3, 4, 5, 6, 8, 10, 12} 中，并且只有在边长为整数的某些条件下，这些等角 n 边形才可以被穹顶化。
A polyiamond is a polygon composed of unit equilateral triangles, and a
generalized deltahedron is a convex polyhedron whose every face is a convex
polyiamond. We study a variant where one face may be an exception. For a convex
polygon P, if there is a convex polyhedron that has P as one face and all the
other faces are convex polyiamonds, then we say that P can be domed. Our main
result is a complete characterization of which equiangular n-gons can be domed:
only if n is in {3, 4, 5, 6, 8, 10, 12}, and only with some conditions on the
integer edge lengths.
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