Knot complements decomposing into prisms
Abstract
We describe four hyperbolic knot complements in S3, each of which covers a prism orbifold: the quotient of H3 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.
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