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arXiv · 2212.12778

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

Nicolas Freeman·Steven Hoehner·Jeff Ledford·David Pack·Brandon Walters
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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.

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Nicolas Freeman, Steven Hoehner, Jeff Ledford, David Pack, Brandon Walters. 2022-12-24. Surface areas of equifacetal polytopes inscribed in the unit sphere $\mathbb{S}^2$. https://doi.org/10.2140/involve.2024.17.311

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