In what I can read of his papers "Densities of regular polytopes, I, II, III" Coxeter defines the "density" of a stellated polytope to be the number of times that it covers (almost) each point of the sphere (if it's centrally projected to the unit sphere). Among all star polygons like the pentagram {5/2}, or {19/8}, density can be any positive integer.* But then things get very interesting: In 3D, the density can be 1, 3, 7. In 4D, the density can be 1, 4, 6, 20, 66, 76, 191. Strange numbers for these highly symmetric situations! —Dan PS I don't have access to the 3 papers of Coxeter mentioned above. If anyone can send (any of) them to me I'd greatly appreciate it. They appear in Proceedings of the Cambridge Philosophical Society v27, 1931, p 201ff; v28, 1932 p 509ff; v29, 1933, p 1ff; respectively. * {p/q} (in lowest terms) denotes the star polygon obtained from dividing the circle into p equal parts and then connecting them with edges between pairs of vertices separated by q of these parts.