Near-Miss Symmetric Polyhedral Cages
Following the experimental discovery of several nearly symmetric protein cages, we define the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages made out of P-gons. We use group theory to parameterize the possible configurations and we minimize the irregularity of the P...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/3/717 |
| _version_ | 1797608811327913984 |
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| author | Bernard M. A. G. Piette Árpad Lukács |
| author_facet | Bernard M. A. G. Piette Árpad Lukács |
| author_sort | Bernard M. A. G. Piette |
| collection | DOAJ |
| description | Following the experimental discovery of several nearly symmetric protein cages, we define the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages made out of P-gons. We use group theory to parameterize the possible configurations and we minimize the irregularity of the P-gons numerically to construct all such polyhedral cages for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>=</mo><mn>6</mn></mrow></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>=</mo><mn>20</mn></mrow></semantics></math></inline-formula> with deformation of up to 10%. |
| first_indexed | 2024-03-11T05:49:51Z |
| format | Article |
| id | doaj.art-05d2610f5ba0458a96bcf3c0001ef5f0 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T05:49:51Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-05d2610f5ba0458a96bcf3c0001ef5f02023-11-17T14:10:00ZengMDPI AGSymmetry2073-89942023-03-0115371710.3390/sym15030717Near-Miss Symmetric Polyhedral CagesBernard M. A. G. Piette0Árpad Lukács1Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UKDepartment of Mathematical Sciences, Durham University, Durham DH1 3LE, UKFollowing the experimental discovery of several nearly symmetric protein cages, we define the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages made out of P-gons. We use group theory to parameterize the possible configurations and we minimize the irregularity of the P-gons numerically to construct all such polyhedral cages for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>=</mo><mn>6</mn></mrow></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>=</mo><mn>20</mn></mrow></semantics></math></inline-formula> with deformation of up to 10%.https://www.mdpi.com/2073-8994/15/3/717uniform polyhedrapolyhedral cagesPlatonic groupnear-miss cagesCayley graphprotein cage |
| spellingShingle | Bernard M. A. G. Piette Árpad Lukács Near-Miss Symmetric Polyhedral Cages Symmetry uniform polyhedra polyhedral cages Platonic group near-miss cages Cayley graph protein cage |
| title | Near-Miss Symmetric Polyhedral Cages |
| title_full | Near-Miss Symmetric Polyhedral Cages |
| title_fullStr | Near-Miss Symmetric Polyhedral Cages |
| title_full_unstemmed | Near-Miss Symmetric Polyhedral Cages |
| title_short | Near-Miss Symmetric Polyhedral Cages |
| title_sort | near miss symmetric polyhedral cages |
| topic | uniform polyhedra polyhedral cages Platonic group near-miss cages Cayley graph protein cage |
| url | https://www.mdpi.com/2073-8994/15/3/717 |
| work_keys_str_mv | AT bernardmagpiette nearmisssymmetricpolyhedralcages AT arpadlukacs nearmisssymmetricpolyhedralcages |