棱锥二面角和的紧界

Pub Date : 2022-06-21 DOI:10.21136/AM.2022.0010-22

Sergey Korotov, Lars Fredrik Lund, Jon Eivind Vatne

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引用次数: 0

摘要

我们证明了具有任意四边形底的金字塔中的八个二面角总是在区间（3π，5π）内加一个数。此外，对于（3π，5π）中的任何数，都存在一个二面角和等于该数的金字塔，这意味着下界和上界是紧的。此外，对于具有平行四边形基的一类金字塔，导出了改进的（且严格的）上界4π。这包括具有矩形底部的棱锥体，通常用于有限元网格生成和分析。

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Tight bounds for the dihedral angle sums of a pyramid

We prove that eight dihedral angles in a pyramid with an arbitrary quadrilateral base always sum up to a number in the interval (3π, 5π). Moreover, for any number in (3π, 5π) there exists a pyramid whose dihedral angle sum is equal to this number, which means that the lower and upper bounds are tight. Furthermore, the improved (and tight) upper bound 4π is derived for the class of pyramids with parallelogramic bases. This includes pyramids with rectangular bases, often used in finite element mesh generation and analysis.

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