Equiprojective polyhedra
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In mathematics, a convex polyhedron is defined to be k {\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 k {\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 k {\displaystyle k} is ( k + 2 ) {\displaystyle (k+2)}-equiprojective. Zonohedra are also equiprojective. Hasan and his colleagues later found more equiprojective polyhedra by truncating equally the tetrahedron and three other Johnson solids.
Hasan & Lubiw (2008) shows there is an O ( n log n ) {\displaystyle O(n\log n)} time algorithm to determine whether a given polyhedron is equiprojective.