Esferas dodecaédricas rómbicas afines

Abstract

Norms Ф are constructed on R³ so that their closed spheres are affine rhombic dodecahedrons D (images of rhombic dodecahedron under an affine automorphism of R³). Conversely, each closed solid D is a unitary sphere with respect to a norm Ф on R³. In both cases Ф is the maximun of six absolute values. This norm yields, in addition to a unified representation, a characterization of the points of the rhombic dodecahedron in terms of the diagonals of the cuboctahedron through its center.