Geometría esférica paraleletópica

Abstract

Norms Ф are constructed on Rⁿ so that the closed spheres with center at G with respect to Ф are n-dimensional parallelotopes of center G. Conversely, for each n-dimensional parallelotope P a norm Ф on Rⁿ is constructed to which P is a closed sphere. In either case Ф is the maximum of n absolute values; and in this way Chebyshev's norn becomes a particular case of Ф. The hiper-cube or measure polytope γ_n is defined and characterized as a locus whose points satisfy a condition.