Surface areas of equifacetal polytopes inscribed in the unit sphere ${\mathbb{S}}^2$

Abstract

This article is concerned with the problem of placing seven or eight points on the unit sphere ${\mathbb{S}}^2$ in ${\mathbb{R}}^3$ so that the surface area of the convex hull of the points is maximized. In each case, the solution is given for convex hulls with congruent isosceles or congruent equilateral triangular facets.

13 pages, 1 table, 15 figures, to appear in Involve, a Journal of Mathematics

References in corpus (3)

• Intrinsic and Dual Volume Deviations of Convex Bodies and Polytopes
• A Concentration Inequality for Random Polytopes, Dirichlet-Voronoi Tiling Numbers and the Geometric Balls and Bins Problem
• The Maximum Surface Area Polyhedron with Five Vertices Inscribed in the Sphere ${\mathbb{S}}^2$