On reduced polytopes and antipodality

DOI10.1515/ADVGEOM.2008.037zbMath1158.52012OpenAlexW2165715344MaRDI QIDQ3546157

Gennadiy Averkov, Horst Martini

Publication date: 18 December 2008

Published in: advg (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/advgeom.2008.037

zbMATH Keywords

thicknessMinkowski spacenormed linear spacepolytopeantipodalityminimum widthreduced bodybody of constant width

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Geometry and structure of normed linear spaces (46B20) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Related Items (8)

Explicit constructions of centrally symmetric \(k\)-neighborly polytopes and large strictly antipodal sets ⋮ Is a complete, reduced set necessarily of constant width? ⋮ Hunting for reduced polytopes ⋮ Reduced convex bodies in Euclidean space -- a survey ⋮ Reduced convex bodies in finite dimensional normed spaces: a survey ⋮ Vertex-facet assignments for polytopes ⋮ A Lipschitz condition for the width function of convex bodies in arbitrary Minkowski spaces ⋮ On pyramids and reducedness

Cites Work

• Reduced bodies in Minkowski space
• The construction and classification of self-dual spherical polyhedra
• Reduced convex bodies in the plane
• Reduced strictly convex plane figure is of constant width
• Antipodality properties of finite sets in Euclidean space
• On the Inequality for Volume and Minkowskian Thickness

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