An upper bound on the shortness exponent of inscribable polytopes (Q1122592)
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scientific article; zbMATH DE number 4106898
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An upper bound on the shortness exponent of inscribable polytopes |
scientific article; zbMATH DE number 4106898 |
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An upper bound on the shortness exponent of inscribable polytopes (English)
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1989
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The author constructs a non-Hamiltonian simplicial 3-polytope with 25 vertices inscribable into the sphere. This polytope is used as a building block for a series of examples showing that the shortness exponent of this class of polytopes is bounded from above by \(\log_ 98\). The series is constructed by the methods of \textit{B. Grünbaum} and \textit{H. Walther} [J. Comb. Theory, Ser. A 14, 364-385 (1973; Zbl 0263.05103)]. The inscribability is proved by realizing the graphs as (augmented) non- degenerate Delaunay triangulations.
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Hamiltonian circuit
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3-polytope
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inscribable
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shortness exponent
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Delaunay triangulations
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0.8815509
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0.87116516
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0.8623378
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0.8616757
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0.8576883
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0.85374403
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