The complement of a hyperbolic knot can described as the union of ideal tetrahedra. An enumeration of knots, based on the number of tetraherda 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, then geodesic lengths are used to break ties.

The initial data is for knots having 7 or fewer tetrahedra in their decompositions. Initial data for knots with 6 or fewer tetrahedra was taken from "The simplest hyperbolic knots" by by Callahan, Dean, and Weeks. Initial data for knots with 7 tetrahedra was taken from "The next simplest hyperbolic knots" by Champanerkar, Kofman, and Patterson.