Bounding minimal solid angles of polytopes

Abstract

In this article we study the following question: What can be the measure of the minimal solid angle of a simplex in ${\mathbb{R}}^d$? We show that in dimensions three it is not greater than the solid angle of the regular simplex. And in dimension four the same holds for simplices sufficiently close to the regular simplex. We also study a similar question for trihedral and dihedral angles of polyhedra compared to those of regular solids.

6 pages

References in corpus (1)

• Bounds for Pach's selection theorem and for the minimum solid angle in a simplex

Cited by in corpus (1)

• Bounds for Pach's selection theorem and for the minimum solid angle in a simplex