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Open AccessArticle

Icosadeltahedral Geometry of Geodesic Domes, Fullerenes and Viruses: A Tutorial on the T-Number

Institute of Physics, Bijenička cesta 46, 10000 Zagreb, Croatia
Symmetry 2020, 12(4), 556; https://doi.org/10.3390/sym12040556
Received: 24 January 2020 / Revised: 10 March 2020 / Accepted: 12 March 2020 / Published: 4 April 2020
(This article belongs to the Special Issue Symmetry in Molecular Biology)
The Caspar–Klug (CK) classification of viruses is discussed by parallel examination of geometry of icosahedral geodesic domes, fullerenes, and viruses. The underlying symmetry of all structures is explained and thoroughly visually represented. Euler’s theorem on polyhedra is used to calculate the number of vertices, edges, and faces in domes, number of atoms, bonds, and pentagonal and hexagonal rings in fullerenes, and number of proteins and protein–protein contacts in viruses. The T-number, the characteristic for the CK classification, is defined and discussed. The superposition of fullerene and dome designs is used to obtain a representation of a CK virus with all the proteins indicated. Some modifications of the CK classifications are sketched, including elongation of the CK blueprint, fusion of two CK blueprints, dodecahedral view of the CK shapes, and generalized CK designs without a clearly visible geometry of the icosahedron. These are compared to cases of existing viruses. View Full-Text
Keywords: virus; fullerene; geodesic dome; T-number virus; fullerene; geodesic dome; T-number
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Šiber, A. Icosadeltahedral Geometry of Geodesic Domes, Fullerenes and Viruses: A Tutorial on the T-Number. Symmetry 2020, 12, 556.

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