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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 |
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Vol. 17 (2024), No. 2, 311–325
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Abstract |
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This article is concerned with the problem of placing seven or eight points on the unit sphere in 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
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Mathematical Subject Classification
Primary: 52A40
Secondary: 52A38, 52B10
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Milestones
Received: 24 December 2022
Accepted: 19 February 2023
Published: 20 May 2024
Communicated by Gaven Martin
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Authors |
| Nicolas Freeman | |
| Department of Mathematics &
Computer Science Longwood University Farmville, VA United States |
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| Steven Hoehner | |
| Department of Mathematics &
Computer Science Longwood University Farmville, VA United States |
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| Jeff Ledford | |
| Department of Mathematics &
Computer Science Longwood University Farmville, VA United States |
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| David Pack | |
| Department of Mathematics &
Computer Science Longwood University Farmville, VA United States |
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| Brandon Walters | |
| Department of Mathematics &
Computer Science Longwood University Farmville, VA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). |
