Right quadruple convexity

Dandan Li, Liping Yuan, Tudor Zamfirescu

Abstract


A set of four points w, x, y, z ∈ Rd (always d ≥ 2) form a rectangular quadruple if their convex hull is a non-degenerate rectangle. The set M is called rq-convex if for every pair of its points we can find another pair in M, such that the four points form a rectangular quadruple. In this paper we start the investigation of rq-convexity in Euclidean spaces.


Keywords


rq-convex sets, parallelotopes, finite sets, Platonic solids

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ISSN: 1855-3974

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