The smallest Haken hyperbolic polyhedra

Atkinson, Christopher; Rafalski, Shawn

doi:10.1090/S0002-9939-2012-11665-X

The smallest Haken hyperbolic polyhedra
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by Christopher K. Atkinson and Shawn Rafalski PDF

Proc. Amer. Math. Soc. 141 (2013), 1393-1404 Request permission

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.

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