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arXiv · 1704.03149

Minimum polyhedron with $n$ vertices

Shigeki Akiyama
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Abstract

We study a polyhedron with $n$ vertices of fixed volume having minimum surface area. Completing the proof of Fejes Toth, we show that all faces of a minimum polyhedron are triangles, and further prove that a minimum polyhedron does not allow deformation of a single vertex. We also present possible minimum shapes for $n\le 12$, some of them are quite unexpected, in particular $n=8$.

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Shigeki Akiyama. 2020-12-18. Minimum polyhedron with $n$ vertices. https://arxiv.org/abs/1704.03149

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