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

Piette, Bernard M. A. G. and Kowalczyk, Agnieszka and Heddle, Jonathan 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). p. 20210679.


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.

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Publisher statement:© 2022 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License, which permits unrestricted use, provided the original author and source are credited.
Date accepted:28 February 2022
Date deposited:07 April 2022
Date of first online publication:06 April 2022
Date first made open access:07 April 2022

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