Antipodality properties of finite sets in Euclidean space

DOI10.1016/j.disc.2004.09.009zbMath1066.52010OpenAlexW1969017194MaRDI QIDQ1772418

Horst Martini, Valeriu Soltan

Publication date: 18 April 2005

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2004.09.009

zbMATH Keywords

Affine diameterAntipodal pointsConvex polytopeDouble normalFinite setMetric diameter

Mathematics Subject Classification ID

Other problems of combinatorial convexity (52A37)

Related Items (16)

On prescribing total orders and preorders to pairwise distances of points in Euclidean space ⋮ The number of double-normals in space ⋮ Nearly \(k\)-distance sets ⋮ On a relative isodiametric inequality for centrally symmetric, compact, convex surfaces ⋮ Explicit constructions of centrally symmetric \(k\)-neighborly polytopes and large strictly antipodal sets ⋮ Geometry where direction matters -- or does it? ⋮ On translative coverings of convex bodies ⋮ On reduced polytopes and antipodality ⋮ Upper bounds for edge-anitpodal and subequilateral polytopes ⋮ Homothetic covering of convex hulls of compact convex sets ⋮ Reduced convex bodies in finite dimensional normed spaces: a survey ⋮ DOUBLE‐NORMAL PAIRS IN SPACE ⋮ Visibility and diameter maximization of convex bodies ⋮ Unit distances and diameters in Euclidean spaces ⋮ Double-normal pairs in the plane and on the sphere ⋮ Large antipodal families

Cites Work

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• Variations on the theme of repeated distances
• Some unsolved problems
• Minimale Durchmesser endlicher Punktmengen mit vorgeschriebenem Mindestabstand
• On finite sets in \(E^ k \)in which the diameter is frequently achieved
• Lower bounds for the numbers of antipodal pairs and strictly antipodal pairs of vertices in a convex polytope
• Shadow-boundaries of convex bodies
• Über zwei Probleme bezüglich konvexer Körper von P. Erdős und von V.L. Klee
• Strictly antipodal sets
• Excursions into combinatorial geometry
• On 6-Point Configurations in 3-Space
• On Sets of Distances of n Points
• On extensive subsets of convex bodies

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