Some New Equiprojective Polyhedra

A convex polyhedron $P$ is $k$-equiprojective if all of its orthogonal projections, i.e., shadows, except those parallel to the faces of $P$ are $k$-gon for some fixed value of $k$. Since 1968, it is an open problem to construct all equiprojective polyhedra. Recently, Hasan and Lubiw [CGTA 40(2):148-155, 2008] have given a characterization of equiprojective polyhedra. Based on their characterization, in this paper we discover some new equiprojective polyhedra by cutting and gluing existing polyhedra.