Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages

Piette, Bernard M.A.G.; Kowalczyk, Agnieszka; Heddle, Jonathan G.

doi:10.1098/rspa.2021.0679

Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages

Piette, Bernard M.A.G.; Kowalczyk, Agnieszka; Heddle, Jonathan G.

Authors

Professor Bernard Piette b.m.a.g.piette@durham.ac.uk
Professor

Agnieszka Kowalczyk

Jonathan G. Heddle

Abstract

Following the discovery of a nearly symmetric protein cage, we introduce the new mathematical concept of a near-miss polyhedral cage (p-cage) as an assembly of nearly regular polygons with holes between them. We then introduce the concept of the connectivity-invariant p-cage and show that they are related to the symmetry of uniform polyhedra. We use this relation, combined with a numerical optimization method, to characterize some classes of near-miss connectivity-invariant p-cages with a deformation below 10% and faces with up to 17 edges.

Citation

Piette, B. M., Kowalczyk, A., & Heddle, J. G. (2022). Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478(2260), Article 20210679. https://doi.org/10.1098/rspa.2021.0679

Journal Article Type	Article
Acceptance Date	Feb 28, 2022
Online Publication Date	Apr 6, 2022
Publication Date	2022-04
Deposit Date	Apr 7, 2022
Publicly Available Date	Apr 7, 2022
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Print ISSN	1364-5021
Electronic ISSN	1471-2946
Publisher	The Royal Society
Peer Reviewed	Peer Reviewed
Volume	478
Issue	2260
Article Number	20210679
DOI	https://doi.org/10.1098/rspa.2021.0679

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© 2022 The Authors.

Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.