Tetrahedral Census Name

The complement of a hyperbolic knot can be described as the union of ideal tetrahedra. An enumeration of knots based on the number of tetrahedra required has been undertaken. The numbering scheme is based first on the number of required tetrahedra and then on volumes. If this is not sufficient, geodesic lengths are used to break ties.

The initial data is for knots with 7 or fewer tetrahedra in their decompositions. Initial data for knots with 6 or fewer tetrahedra was taken from [1]. Initial data for knots with 7 tetrahedra was taken from [2].

References

[1] Callahan, P. J., Dean, J. C., and Weeks, J. R., "The simplest hyperbolic knots".

[2] Champanerkar, A., Kofman, I., and Patterson, E., "The next simplest hyperbolic knots".