The complete $10$-tetrahedra census of orientable cusped hyperbolic $3$-manifolds

Abstract

We extend the complete census of orientable cusped hyperbolic $3$-manifolds to $10$ tetrahedra, giving the next $150730$ manifolds and their $496638$ minimal ideal triangulations. As applications, we find the precisely $439898$ exceptional Dehn fillings on them, revealing the next $1849$ simplest hyperbolic knot exteriors in $S^3$. We also give the simplest example of an orientable cusped hyperbolic $3$-manifold containing a closed totally geodesic surface.

arXiv comment16 pages, to appear in Proceedings of the 42nd International Symposium on Computational Geometry (SoCG 2026)