Open AccessCharacterization of near-miss connectivity-invariant homogeneous convex polyhedral cages
Author(s) -
Bernard Piette,
Agnieszka Kowalczyk,
Jonathan G. Heddle
Publication year - 2022
Publication title -
proceedings - royal society. mathematical, physical and engineering sciences
Language(s) - English
Resource type - Journals
eISSN - 1471-2946
pISSN - 1364-5021
DOI - 10.1098/rspa.2021.0679
Subject(s) - polyhedron , cage , invariant (physics) , regular polygon , homogeneous , combinatorics , mathematics , computer science , geometry , mathematical physics
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.