Geodesic
Tight bounds for the dihedral angle sums of a pyramid
Applications of Mathematics, Tome 68 (2023) no. 3, pp. 259-268

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We prove that eight dihedral angles in a pyramid with an arbitrary quadrilateral base always sum up to a number in the interval $(3\pi ,5\pi )$. Moreover, for any number in $(3\pi ,5\pi )$ 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 $4\pi $ 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.
DOI : 10.21136/AM.2022.0010-22
Classification : 51M20, 52B10
Keywords: pyramid; dihedral angle sum; tight angle bounds 
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Korotov, Sergey; Lund, Lars Fredrik; Vatne, Jon Eivind. Tight bounds for the dihedral angle sums of a pyramid. Applications of Mathematics, Tome 68 (2023) no. 3, pp. 259-268. doi: 10.21136/AM.2022.0010-22

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