Mixed-platonic 3-manifolds

Eric Chesebro; Michelle Chu; Jason Deblois; Neil R. Hoffman; Priyadip Mondal; Genevieve S. Walsh

doi:10.2140/agt.2026.26.2215

Mixed-platonic 3-manifolds

Eric Chesebro
, Michelle Chu
, Jason Deblois
, Neil R. Hoffman
, Priyadip Mondal
, Genevieve S. Walsh

Mathematical Sciences

University of Minnesota Twin Cities
University of Pittsburgh
University of Minnesota Duluth
Ben-Gurion University of the Negev
Tufts University

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a class of cusped hyperbolic 3-manifolds that we call mixed-platonic, composed of regular ideal hyperbolic polyhedra of more than one type, which includes certain previously known examples. We establish basic facts about mixed-platonic manifolds which allow us to conclude, among other things, that there is no mixed-platonic hyperbolic knot complement with hidden symmetries.

Original language	English
Pages (from-to)	2215-2254
Number of pages	40
Journal	Algebraic and Geometric Topology
Volume	26
Issue number	6
DOIs	https://doi.org/10.2140/agt.2026.26.2215
State	Published - Jun 22 2026

Keywords

hidden symmetries
hyperbolic 3-manifolds
hyperbolic orbifolds
knot complements

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10.2140/agt.2026.26.2215

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abstract = "We introduce a class of cusped hyperbolic 3-manifolds that we call mixed-platonic, composed of regular ideal hyperbolic polyhedra of more than one type, which includes certain previously known examples. We establish basic facts about mixed-platonic manifolds which allow us to conclude, among other things, that there is no mixed-platonic hyperbolic knot complement with hidden symmetries.",

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author = "Eric Chesebro and Michelle Chu and Jason Deblois and Hoffman, \{Neil R.\} and Priyadip Mondal and Walsh, \{Genevieve S.\}",

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AU - Chesebro, Eric

AU - Chu, Michelle

AU - Deblois, Jason

AU - Hoffman, Neil R.

AU - Mondal, Priyadip

AU - Walsh, Genevieve S.

PY - 2026/6/22

Y1 - 2026/6/22

N2 - We introduce a class of cusped hyperbolic 3-manifolds that we call mixed-platonic, composed of regular ideal hyperbolic polyhedra of more than one type, which includes certain previously known examples. We establish basic facts about mixed-platonic manifolds which allow us to conclude, among other things, that there is no mixed-platonic hyperbolic knot complement with hidden symmetries.

AB - We introduce a class of cusped hyperbolic 3-manifolds that we call mixed-platonic, composed of regular ideal hyperbolic polyhedra of more than one type, which includes certain previously known examples. We establish basic facts about mixed-platonic manifolds which allow us to conclude, among other things, that there is no mixed-platonic hyperbolic knot complement with hidden symmetries.

KW - hidden symmetries

KW - hyperbolic 3-manifolds

KW - hyperbolic orbifolds

KW - knot complements

UR - https://www.scopus.com/pages/publications/105043721714

U2 - 10.2140/agt.2026.26.2215

DO - 10.2140/agt.2026.26.2215

M3 - Article

AN - SCOPUS:105043721714

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SP - 2215

EP - 2254

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 6

ER -

Mixed-platonic 3-manifolds

Abstract

Keywords

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