Faculty of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
Copyright © 2010 Hiroaki Kido. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A subset in the -dimensional Euclidean space that contains points (elements) is
called an -point isosceles set if every triplet of points selected from them forms an isosceles
triangle. In this paper, we show that there exist exactly two 11-point isosceles sets in up to
isomorphisms and that the maximum cardinality of isosceles sets in is 11.