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.
