The Number of Hexagons and the Simplicity of Geodesics on Certain Polyhedra

Abstract

The problem of determining the possible morphological types of convex polyhedra in three-dimensional Euclidean space E3 is well known to be quite hopeless. We lack not only any general way of determining whether there exists a convex polyhedron having as faces ƒ3 triangles, ƒ4 quadrangles, . . . , and ƒnn-gons, but even much more special questions of this kind seem to be rather elusive.