Tight bounds for the dihedral angle sums of a pyramid
Peer reviewed, Journal article
Published version
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https://hdl.handle.net/11250/3065423Utgivelsesdato
2022Metadata
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Sammendrag
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.