Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)2022-03-142022-03-14https://noesis.uis.edu.co/handle/20.500.14071/7183A class Rn of central n-dimensional 2n-topes named Bn and norms F are coined so that the closed spheres with respect to F are polytopes Bn. Conversely, each Bn is* closed unitary sphere with respect to a norm F on Rn. In both cases F is the sum of n absolute values, so that F is a generalization of the norm inducing the taxi-cab metric. Particulary the cross polytope Bn belongs to Bn and B3 is just the family of the centrally symmetric solid octahedra. Bn is defined and characterized as a locus whose points satisfy a metric condition.application/pdfinfo:eu-repo/semantics/articlehttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)