On Isosceles Sets in the 4-Dimensional Euclidean Space

Abstract EN

A subset X in the k-dimensional Euclidean space ℝk that contains n points (elements) is called an n-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 ℝ4 up to isomorphisms and that the maximum cardinality of isosceles sets in ℝ4 is 11.