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

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arXiv · 2407.01708

Mixed-platonic 3-manifolds

Eric Chesebro·Michelle Chu·Jason DeBlois·Neil R. Hoffman·Priyadip Mondal·Genevieve S. Walsh

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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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Eric Chesebro, Michelle Chu, Jason DeBlois, Neil R. Hoffman, Priyadip Mondal, Genevieve S. Walsh. 2024-07-01. Mixed-platonic 3-manifolds. https://doi.org/10.2140/agt.2026.26.2215

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