Steinhaus Conditions for Convex Polyhedra

Autor:	Joël Rouyer
Rok vydání:	2016
Předmět:	Combinatorics Polyhedron Dense set Convex polytope Regular polygon Mathematics::Metric Geometry Antipodal point Mathematics Intrinsic metric
Zdroj:	Convexity and Discrete Geometry Including Graph Theory ISBN: 9783319281841
DOI:	10.1007/978-3-319-28186-5_7
Popis:	On a convex surface S, the antipodal map F associates to any point p in S the set of farthest points from p, with respect to the intrinsic metric. S is called a Steinhaus surface if F is a single-valued involution. We prove that any convex polyhedron has an open and dense set of points p admitting a unique antipode \(F_{p}\), which in turn admits a unique antipode \(F_{F_{p}}\), distinct from p. In particular, no convex polyhedron is Steinhaus.
Databáze:	OpenAIRE
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