[Cos-top] Jesper tells why

P.P.S. I like Jesper's response because it hints at *why* the various levels contain the number of dodecahedra that they do. In effect, Jesper is showing the relation between the binary icosahedral group (which is the holonomy group of the Poincaré dodecahedral space) and the ordinary dodecahedral group (the symmetries of the original dodecahedron at layer 1). The relationship, which Jesper's table clearly shows, is that if you travel in the direction of a symmetry axis (of the original layer 1 dodecahedron) of order n, you'll find 2n translates of the dodecahedron spaced pi/n radians apart.

This same relation holds, of course, for the other single-action spherical manifolds.