Bi-Symmetric Polyhedral Cages with Maximally Connected Faces and Small Holes

Piette, Bernard; Lukács, Árpad

Abstract

Polyhedral cages (p-cages) describe the geometry of some families of artificial protein cages. We identify the p-cages made out of families of equivalent polygonal faces such that the faces of one family have five neighbors and P1 edges, while those of the other family have six neighbors and P2 edges. We restrict ourselves to polyhedral cages where the holes are adjacent to four faces at most. We characterize all p-cages with a deformation of the faces, compared to regular polygons, not exceeding 10%.

Citation

Piette, B., & Lukács, Á. (2025). Bi-Symmetric Polyhedral Cages with Maximally Connected Faces and Small Holes. Symmetry, 17(1), Article 101. https://doi.org/10.3390/sym17010101

• Journal Article Type: Article
• Acceptance Date: Jan 8, 2025
• Online Publication Date: Jan 10, 2025
• Publication Date: 2025-01
• Deposit Date: Jan 31, 2025
• Publicly Available Date: Jan 31, 2025
• Journal: Symmetry
• Electronic ISSN: 2073-8994
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 1
• Article Number: 101
• DOI: https://doi.org/10.3390/sym17010101
• Keywords: polyhedral cages, platonic group, Cayley graph, protein cage, nano-cage, uniform polyhedra, nanoparticle, near-miss cages, capsid
• Public URL: https://durham-repository.worktribe.com/output/3362578