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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The smallest Haken hyperbolic polyhedra


Authors: Christopher K. Atkinson and Shawn Rafalski
Journal: Proc. Amer. Math. Soc. 141 (2013), 1393-1404
MSC (2010): Primary 52B10, 57M50, 57R18
Published electronically: September 5, 2012
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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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Additional Information

Christopher K. Atkinson
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19106
Email: ckatkin@temple.edu

Shawn Rafalski
Affiliation: Department of Mathematics and Computer Science, Fairfield University, Fairfield, Connecticut 06824
Email: srafalski@fairfield.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11665-X
PII: S 0002-9939(2012)11665-X
Keywords: Hyperbolic polyhedra, 3–dimensional Coxeter polyhedra, hyperbolic orbifold, polyhedral orbifold, hyperbolic volume, Haken orbifold
Received by editor(s): August 19, 2011
Published electronically: September 5, 2012
Communicated by: Michael Wolf
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.