| Abstrakt: |
Abstract: 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. |
