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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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8984814 | PMC |
| http://dx.doi.org/10.1098/rspa.2021.0679 | DOI Listing |
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Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages.
Proc Math Phys Eng Sci
April 2022
Malopolska Centre of Biotechnology, Jagiellonian University, Gronostajowa 7A, Krakow 30-387, Poland.
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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