Geodesic
Tight bounds for the dihedral angle sums of a pyramid
Applications of Mathematics, Tome 68 (2023) no. 3, pp. 259-268 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     title = {Tight bounds for the dihedral angle sums of a pyramid},
     journal = {Applications of Mathematics},
     pages = {259--268},
     year = {2023},
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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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