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Tight bounds for the dihedral angle sums of a pyramid

Sergey Korotov, Lars Fredrik Lund, Jon Eivind Vatne (2023)

Applications of Mathematics

We prove that eight dihedral angles in a pyramid with an arbitrary quadrilateral base always sum up to a number in the interval ( 3 π , 5 π ) . Moreover, for any number in ( 3 π , 5 π ) 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 π is derived for the class of pyramids with parallelogramic bases. This includes pyramids with rectangular bases, often used in finite element mesh generation and...

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