Near-Miss Bi-Homogenous Symmetric Polyhedral Cages

Piette, Bernard; Lukács, Árpad

Abstract

Following the discovery of an artificial protein cage with a paradoxical geometry, we extend the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages, for which all the faces are equivalent, and define bi-homogeneous symmetric polyhedral cages made of two different types of faces, where all the faces of a given type are equivalent. We parametrise the possible connectivity configurations for such cages, analytically derive p-cages that are regular, and numerically compute near-symmetric p-cages made of polygons with 6 to 18 edges and with deformation not exceeding 10%.

Citation

Piette, B., & Lukács, Á. (2023). Near-Miss Bi-Homogenous Symmetric Polyhedral Cages. Symmetry, 15(9), Article 1804. https://doi.org/10.3390/sym15091804

• Journal Article Type: Article
• Acceptance Date: Sep 13, 2023
• Online Publication Date: Sep 21, 2023
• Publication Date: 2023-09
• Deposit Date: Oct 18, 2023
• Publicly Available Date: Oct 18, 2023
• Journal: Symmetry
• Electronic ISSN: 2073-8994
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 15
• Issue: 9
• Article Number: 1804
• DOI: https://doi.org/10.3390/sym15091804
• Keywords: Cayley graph, nanoparticle, uniform polyhedra, polyhedral cages, platonic group, protein cage, nanocage, near-miss cages
• Public URL: https://durham-repository.worktribe.com/output/1797862