Re: [math-fun] "Density" of a regular polytope

PS An extremely kind math-fun member has forwarded to me copies of these papers — so I no longer need to acquire them. —Dan ----- 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! -----