Alternative proof of Sine's theorem on the size of a regular polygon in \(\mathbb{R}{}^ n\) with the \(\ell{}_ \infty\)-metric
Le \((A,d)\) be a finite metric space with a transitive group of isometries. Furthermore suppose that \((A,d)\) is isometrically embeddable into \(\mathbb{R}^ n\) endowed with the \(l_ \infty\)-norm. The authors show that this implies that \(A\) has at most \((2n)^ n\) elements. Hence every regular \(m\)-gon in \((\mathbb{R}^ n,l_ \infty)\) has at most \((2n)^ n\) vertices.
scientific article; zbMATH DE number 54919