An upper bound on the shortness exponent of inscribable polytopes
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.
scientific article; zbMATH DE number 4106898
scientific article