speedfreek: Your reference to the Poincare conjecture induced me to Google it to find out what it claims. I had of course heard of it earlier but had never managed to find out what it claimed, even after it had made a big splash in the news several years ago on finally being proven. I had supposed it to be an abstract idea in pure mathematics of no immediate interest to cosmologists.

The same seemed to apply to the supposed relevance of the dodecahedron to cosmology. From the reference you cited, I learned that the conceivable relevance of the dodecahedron is the same as for the 3-torus when parallel faces or the former are "glued" in the topological sense. I still feel that the glued dodecahedron, like the 3-torus, is too implausible to be taken seriously as a possible model for the Universe.