Every Tetrahedron has a 3-vertex Quasigeodesic

TL;DR

This paper proves that every tetrahedron contains a simple, closed quasigeodesic passing through three vertices, showing a universal geometric property related to exterior angles.

Contribution

It establishes the existence of a 3-vertex quasigeodesic in every tetrahedron, a new geometric result in polyhedral theory.

Findings

Existence of a 3-vertex quasigeodesic in all tetrahedra

Every tetrahedron has a face with exterior angles at most pi

Universal geometric property proven for tetrahedra

Abstract

We prove that every tetrahedron T has a simple, closed quasigeodesic that passes through three vertices of T. Equivalently, every T has a face whose "exterior angles" are at most pi.