The Maximum Surface Area Polyhedron with Five Vertices Inscribed in the Sphere S2
We determine the optimal placement of five points on a unit sphere so that the surface area of the convex hull of the points is maximized. Furthermore, we showed that the optimal polytope is a triangular bipyramid with two of the five points placed at the north and south poles and the other three forming an equilateral triangle inscribed in the equator.
Donahue, Jessica, "The Maximum Surface Area Polyhedron with Five Vertices Inscribed in the Sphere S2" (2020). Fall Showcase for Research and Creative Inquiry. 59.