Daniel Moskovich recently wrote about the discovery by a lawyer of a duplication in the knot tables called the “Perko pair”.
Now a banker has found another duplicate in yet another table of 3-manifolds. This time it was Ben Burton, and the duplicate appears in the Hildebrand-Weeks cusped hyperbolic census.
I’m exaggerating a little. Ben is no longer a banker. But the duplication is real. The problem is that SnapPea’s Epstein-Penner decomposition code sometimes has trouble with highly symmetric manifolds. If the Epstein-Penner decomposition is not a triangulation, SnapPea attempts to build a subdivision. Unfortunately it does not always build a canonical-such subdivision. In this particular case, SnapPea generated distinct 5-tetrahedron subdivisions of a cube. Somehow the duplication was missed.
The problem resulted in a repeated manifold in the census.