Resumen: In a recent work of Alessandro Fonda, a generalization of the parallelogram law in any dimension N >= 2 was given by considering the ratio of the quadratic mean of the measures of the (N - 1)-dimensional diagonals to the quadratic mean of the measures of the faces of a parallelotope. In this paper, we provide a further generalization considering not only (N - 1)-dimensional diagonals and faces, but the k-dimensional ones for every 1 <= k <= N - 1. Idioma: Inglés Año: 2020 Publicado en: CONTRIBUTIONS TO DISCRETE MATHEMATICS 15, 2 (2020), 153-158 ISSN: 1715-0868 Originalmente disponible en: Texto completo de la revista