A New Polyhedral Approximation to an Ellipsoid of Revolution

Abstract

A polyhedral structure is described which differs from the usual geodesic structure (in which the vertices lie on the surface of revolution), in that each edge is tangent to the surface. This new edge-tangent (geotangent) polyhedron has the following advantages over the usual geodesic design with its triangular faces: (1) the equatorial ring of faces is normal to the equatorial plane; (2) the faces are (with minor exceptions) pentagons and hexagons; (3) only three or four edges meet at each vertex; (4) calculation of edge lengths, vertex angles, and low-profile structures is comparatively easy. This ease of computation is a consequence of the fact that the constraints which define the structure make it simple to specify the equations of the polyhedral faces. These constraints are fully described in this paper, and examples of the structure are given. A template from which a paper model can be constructed is included.