I was going through Bill Thurston's "The Geometry and Topology of 3-Manifolds" (specifically Ch. 7: http://library.msri.org/books/gt3m/PDF/7.pdf). Along with Wikipedia (which uses it as a source), it mentions that the complement of the Borromean rings are homeomorphic to 2 ideal octahedra glued together. However, I watched the video "Not Knot," which claims that the complement of the Borromean rings is homeomorphic to a rhombic dodecahedron. I am inclined to believe Thurston, however I came across https://www.ias.edu/ideas/2016/agol-hyperbolic-link-complements, which was written by Ian Agol. It shares a rendition of the complement of the Borromean rings, which seems to be an ideal version of a rhombic dodecahedron (if that is a thing). Are these two things the same thing? If not, what is their relation or why the discrepancy?
2026-03-30 06:50:14.1774853414
Discrepancy in sources of the complement of the Borromean rings?
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