Combinatorial geometry of belt bodies

DOI10.1007/BF03322255zbMath0853.52004OpenAlexW1993604621MaRDI QIDQ1904436

Horst Martini, Vladimir G. Boltyanski

Publication date: 1 February 1996

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

Full work available at URL: https://doi.org/10.1007/bf03322255

zbMATH Keywords

illuminationzonoidbelt bodycovering problemHelly dimensionfixing systembelt polytopeequatorial polytope

Mathematics Subject Classification ID

Other problems of combinatorial convexity (52A37) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Helly-type theorems and geometric transversal theory (52A35) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (6)

Improved bounds for Hadwiger's covering problem via thin-shell estimates ⋮ Covering convex hulls of compact convex sets with smaller homothetic copies ⋮ On the multiple illumination numbers of convex bodies ⋮ Covering functionals of Minkowski sums and direct sums of convex bodies ⋮ Carathéodory's theorem and \(H\)-convexity ⋮ On covering functionals of convex bodies

Cites Work

• Fixing system and homothetic covering
• On the Aleksandrov-Fenchel inequality involving zonoids
• A new step in the solution of the Szökefalvi-Nagy problem
• A solution of Hadwiger's covering problem for zonoids
• Solution of the Szökefalvi-Nagy problem for a class of convex polytopes
• SIX-POINT PRIMITIVE FIXING SYSTEM IN A PLANE
• On primitive polyhedra
• Zonohedra and Generalized Zonohedra
• A support characterization of zonotopes
• Fixing systems and inner illumination
• A Class of Convex Bodies
• On polytopes fixed by their vertices
• Solution of the illumination problem for bodies with md \(M=2\)
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