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Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages
Bernard M A G Piette1, Agnieszka Kowalczyk2,3, Jonathan G Heddle2
1Department of Mathematical Sciences, Durham University, South Road, Durham DH1 3LE, UK.
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.
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