Isosceles triple convexity

Liping Yuan, Tudor Zamfirescu, Yue Zhang

A set SS in RdRd is called itit-convex if, for any two distinct points in SS, there exists a third point in SS, such that one of the three points is equidistant from the others. In this paper we first investigate nondiscrete itit-convex sets, then discuss about the itit-convexity of the eleven Archimedean tilings, and treat subsequently finite subsets of the square lattice. Finally, we obtain a lower bound on the number of isosceles triples contained in an nn-point itit-convex set.

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Zhang, Yue, Yuan, Liping, Zamfirescu, Tudor