Esferas hiperoctaédricas centralmente simétricas

Abstract

A class R_n of central n-dimensional 2ⁿ-topes named B_n and norms F are coined so that the closed spheres with respect to F are polytopes B_n. Conversely, each B_n 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 B_n belongs to B_n and B₃ is just the family of the centrally symmetric solid octahedra. B_n is defined and characterized as a locus whose points satisfy a metric condition.