Magic twin body stars generated from chains of prismoids

There is a vertex-labeling with different integers for the compound of two tetrahedra such that the values on an edge always deliver the same magic sum. We investigate stars composed of a polyhedron and its dual where the generating polyhedron consists of a chain of w-sided prismoids. Let the resulting 3-uniform hypergraph show h latitudinal rings of points including the poles. Then a magic vertex-labeling exists iff h=w+1. Supermagic labeling is excluded. Examples up to w=6 are presented.