On knot complements that decompose into regular ideal dodecahedra

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Abstract

Aitchison and Rubinstein showed there are two distinct ways to identify the faces of a pair of regular ideal dodecahedra and obtain a knot complement. This paper shows that these knot complements are the only knot complements that decompose into $$n$$n regular ideal dodecahedra, providing a partial solution to a conjecture of Neumann and Reid. A corollary of the main theorem classifies the hyperbolic knot complements can be decomposed into regular ideal polyhedra.

Original languageEnglish (US)
Pages (from-to)299-308
Number of pages10
JournalGeometriae Dedicata
Volume173
Issue number1
DOIs
StatePublished - Dec 1 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2013, Springer Science+Business Media Dordrecht.

Keywords

  • Commensurability
  • Dodecahedral knots
  • Hidden symmetries

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