Two-sided bounds for dihedral angle sums of path and 4-ball tetrahedra

Abstract

A tetrahedron is called a path tetrahedron, if it has three mutually orthogonal edges that do not intersect at a single point. A tetrahedron is called a 4-ball tetrahedron, if there exists a sphere tangent to all its edges. We derive two-sided tight bounds for dihedral angle sums of such tetrahedra. In particular, we prove that this sum lies in the interval (2{\pi}, 2.5{\pi}) for path tetrahedra and in [6 arccos 1/3, 3{\pi}) for 4-ball tetrahedra. Also some of their useful properties are presented.