p-环面最小三三角剖分

IF 0.8 4区数学 Q2 MATHEMATICS

Filomat Pub Date : 2023-01-01 DOI:10.2298/fil2301115s

M. Stojanovic

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引用次数: 0

摘要

众所周知，凸多面体总是可以用3-三角形(即用原始顶点划分为四面体)，但非凸多面体却不一定。多面体拓扑上等同于带p柄的球，简称p环面，不能是凸的。因此，研究它们的3-三角剖分的可能性和性质是很有趣的。本文研究了可三三角形p-环面三角剖分所需的最小四面体数。为此，我们提出了分段凸多面体及其连接图的概念。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Minimal 3-triangulations of p-toroids

It is known that we can always 3-triangulate (i.e. divide into tetrahedra with the original vertices) convex polyhedra but not always non-convex ones. Polyhedra topologically equivalent to ball with p handles, shortly p-toroids, cannot be convex. So, it is interesting to investigate possibilities and properties of their 3-triangulations. Here we study the minimal number of necessary tetrahedra for the triangulation of a 3-triangulable p-toroid. For that purpose, we developed the concept of piecewise convex polyhedron and that of its connection graph.

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