Magic twin body stars generated from chains of prismoids (Q1398277)

A hypergraph \(H=(V,E)\) is magic, if there is an injective labeling of the vertices with positive integers, such that each hyperedge has the same sum of the labels of the vertices in it. It is supermagic if the labeling also is a bijection to \(\{1, \dots, |V|\}\). This paper studies for certain hypergraphs whether they are magic or supermagic: stars composed of a polyhedron and its dual where the generating polyhedron consists of a chain of \(w\)-side prismoids. Each hyperedge contains three vertices. The characterization is as follows: Suppose it shows \(h\) latitudinal rinds of points including the points. Then the hypergraph is magic if and only if \(h=w+1\). These hypergraphs are never supermagic.