Surface areas of equifacetal polytopes inscribed in the unit sphere $\mathbb{S}^2$
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
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| _version_ | 1866909207399235584 |
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| author | Freeman, Nicolas Hoehner, Steven Ledford, Jeff Pack, David Walters, Brandon |
| author_facet | Freeman, Nicolas Hoehner, Steven Ledford, Jeff Pack, David Walters, Brandon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12778 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Surface areas of equifacetal polytopes inscribed in the unit sphere $\mathbb{S}^2$ Freeman, Nicolas Hoehner, Steven Ledford, Jeff Pack, David Walters, Brandon Metric Geometry 52A40 (Primary) 52A38, 52B10 (Secondary) 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. |
| title | Surface areas of equifacetal polytopes inscribed in the unit sphere $\mathbb{S}^2$ |
| topic | Metric Geometry 52A40 (Primary) 52A38, 52B10 (Secondary) |
| url | https://arxiv.org/abs/2212.12778 |