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

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

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
• Public URL: https://durham-repository.worktribe.com/output/1210496