Combination Stitch Doctor Who also 12-Sided Die

Each of the twelve enumerated incarnations from the Doctor appear on Robin’s 5-inch tall dodecahedron which is charmingly cross stitched in vibrant colors. She writes that the numbers on opposing sides add up to 13, so presumably Peter Davidson is opposite  Paul McGann, and so forth.

The War Doctor is, I gather, not integrated. Could one created a 13-sided polyhedron with identical faces? I amnot sure. One could certainly do so with non-identical faces. But I was hired to work at Neatorama for my good looks, not my math abilities.