Knot complements decomposing into prisms

Abstract

We describe four hyperbolic knot complements in ${\mathbb{S}}^3$, each of which covers a prism orbifold: the quotient of ${\mathbb{H}}^3$ by the action of a discrete group generated by reflections in the faces of a polyhedron that has the combinatorial type of a triangular prism. The prism orbifolds are rigid-cusped and contain compact, totally geodesic hyperbolic triangle sub-orbifolds; as a result, the knot complements covering them have hidden symmetries and contain closed, embedded, totally geodesic surfaces.

57 pages, 18 figures, 7 tables, supporting code in ancillary files. Version 2 has minor changes from the previous version reflecting suggestions from a referee. These changes include better references to the ancillary files and additional exposition, as well as the correction of a typo in Table 4 and a computational error in the proof of Lemma 5.5