On isosceles sets in the 4-dimensional Euclidean space (Q541180)

Summary: A subset \(X\) in the \(k\)-dimensional Euclidean space \(\mathbb R^k\) 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 \(\mathbb R^4\) up to isomorphisms and that the maximum cardinality of isosceles sets in \(\mathbb R^4\) is 11.