Equiprojective polyhedra

In mathematics, a convex polyhedron is defined to be ${\displaystyle k}$-equiprojective if every orthogonal projection of the polygon onto a plane, in a direction not parallel to a face of the polyhedron, forms a ${\displaystyle k}$-gon. For example, a cube is 6-equiprojective: every projection not parallel to a face forms a hexagon, More generally, every prism over a convex ${\displaystyle k}$ is ${\displaystyle (k+2)}$-equiprojective.^[1][2] Zonohedra are also equiprojective.^[3] Hasan and his colleagues later found more equiprojective polyhedra by truncating equally the tetrahedron and three other Johnson solids.^[4]

Hasan & Lubiw (2008) shows there is an ${\displaystyle O(n\log n)}$ time algorithm to determine whether a given polyhedron is equiprojective.^[5]