Ball polytopes and the Vázsonyi problem

DOI10.1007/s10474-009-9030-0zbMath1224.52025arXiv0905.1528OpenAlexW2067089166MaRDI QIDQ624221

Horst Martini, Micha A. Perles, Yaakov S. Kupitz

Publication date: 8 February 2011

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.1528

zbMATH Keywords

geometric graphspherical convexitybarycentric subdivisiondiameter graphball hullball polytopecanonical self-dualityface complexface structuregeneralized convexity notioninvolutory self-dualityReuleaux polytopespindle convexityVázsonyi problem

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Three-dimensional polytopes (52B10) Inequalities and extremum problems involving convexity in convex geometry (52A40) Erd?s problems and related topics of discrete geometry (52C10) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items (17)

An analogue of a theorem of Steinitz for ball polyhedra in \(\mathbb{R}^3\) ⋮ Dowker-type theorems for hyperconvex discs ⋮ Ball convex bodies in Minkowski spaces ⋮ On Random Disc Polygons in Smooth Convex Discs ⋮ On the intrinsic volumes of intersections of congruent balls ⋮ Complete sets in normed linear spaces ⋮ From \(r\)-dual sets to uniform contractions ⋮ Ball and spindle convexity with respect to a convex body ⋮ Peabodies of constant width ⋮ Rigid ball-polyhedra in Euclidean 3-space ⋮ Meissner polyhedra ⋮ Inequalities for hyperconvex sets ⋮ The graphs behind reuleaux polyhedra ⋮ Strongly involutive self-dual polyhedra ⋮ On the multiple Borsuk numbers of sets ⋮ Volumetric bounds for intersections of congruent balls in Euclidean spaces ⋮ 𝑑-dimensional self-dual polytopes and Meissner polytopes

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