2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131272The positive interpoint distances of n=p+1>1 points in dimension p are equal if and only if their sample covariance matrix is a scalar multiple of the identity.5 pages, which includes corrections to the published version. Version 2 differs in only small typographical changes: removing an extra sigma squared, and inserting a needed 1/nStatistics TheoryMetric Geometry62-07,51F20text