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Polyhedra and packings from hyperbolic honeycombs

Pedersen, Martin; Hyde, Stephen


We derive more than 80 embeddings of 2D hyperbolic honeycombs in Euclidean 3 space, forming 3-periodic infinite polyhedra with cubic symmetry. All embeddings are “minimally frustrated,” formed by removing just enough isometries of the (regular, but unphysical) 2D hyperbolic honeycombs {3, 7}, {3, 8}, {3, 9}, {3, 10}, and {3, 12} to allow embeddings in Euclidean 3 space. Nearly all of these triangulated “simplicial polyhedra” have symmetrically identical vertices, and most are chiral. The...[Show more]

CollectionsANU Research Publications
Date published: 2018
Type: Journal article
Source: PNAS - Proceedings of the National Academy of Sciences of the United States of America
DOI: 10.1073/pnas.1720307115


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