Sufficiently Fat Polyhedra are not 2-castable

Abstract

In this note we consider the problem of manufacturing a convex polyhedral object via casting. We consider a generalization of the sand casting process where the object is manufactured by gluing together two identical faces of parts cast with a single piece mold. In this model we show that the class of convex polyhedra which can be enclosed between two concentric spheres of the ratio of their radii less than 1.07 cannot be manufactured using only two cast parts.