Abstract: An polytope model includes a plurality of polyhedral elements, each element having a plurality of slanted faces and a base. The slanted faces meet at a common apex. For example, the polyhedral elements may be n-gon pyramids. In one embodiment, the polyhedral elements are identical. In alternative embodiments, the elements may define multiple distinct polyhedrons. The polyhedral elements are arranged such that the slanted faces of each element are disposed adjacent the slanted faces of other elements. The bases of the arranged polyhedral elements form the facets of a formed polyhedron. In one embodiment, the polyhedral elements are square pyramids such that the formed polyhedron is a cube wherein the faces of the cube are the bases of the square pyramids.