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

Nicolas Freeman, Steven Hoehner, Jeff Ledford, David Pack and Brandon Walters

Vol. 17 (2024), No. 2, 311–325
Abstract

This article is concerned with the problem of placing seven or eight points on the unit sphere 𝕊2 in 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.

Keywords
bipyramid, equifacetal, polyhedron, polytope, surface area
Mathematical Subject Classification
Primary: 52A40
Secondary: 52A38, 52B10
Milestones
Received: 24 December 2022
Accepted: 19 February 2023
Published: 20 May 2024

Communicated by Gaven Martin
Authors
Nicolas Freeman
Department of Mathematics & Computer Science
Longwood University
Farmville, VA
United States
Steven Hoehner
Department of Mathematics & Computer Science
Longwood University
Farmville, VA
United States
Jeff Ledford
Department of Mathematics & Computer Science
Longwood University
Farmville, VA
United States
David Pack
Department of Mathematics & Computer Science
Longwood University
Farmville, VA
United States
Brandon Walters
Department of Mathematics & Computer Science
Longwood University
Farmville, VA
United States