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

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