The smallest Haken hyperbolic polyhedra

Shawn Rafalski (Fairfield)

Abstract: We determine the lowest volume hyperbolic Coxeter polyhedron whose corresponding hyperbolic polyhedral 3–orbifold contains an essential 2-suborbifold, up to a canonical decomposition along essential hyperbolic triangle 2–suborbifolds. This is joint work with Chris Atkinson (Temple University).