Editing Capsid (section)

===Icosahedral===
[[File:Adenovirus 3D schematic.png|thumb|Icosahedral capsid of an [[Adenoviridae|adenovirus]]]]
[[File:Virus capsid T number.tif|thumb|right|Virus capsid T-numbers]]
The icosahedral structure is extremely common among viruses. The [[icosahedron]] consists of 20 triangular faces delimited by 12 fivefold vertexes and consists of 60 asymmetric units. Thus, an icosahedral virus is made of 60N protein subunits. The number and arrangement of [[capsomere]]s in an icosahedral capsid can be classified using the "quasi-equivalence principle" proposed by [[Donald Caspar]] and [[Aaron Klug]].<ref name=Caspar1962>{{cite journal | vauthors = Caspar DL, Klug A | title = Physical principles in the construction of regular viruses | journal = Cold Spring Harbor Symposia on Quantitative Biology | volume = 27 | pages = 1–24 | year = 1962 | pmid = 14019094 | doi = 10.1101/sqb.1962.027.001.005 }}</ref> Like the [[Goldberg polyhedra]], an icosahedral structure can be regarded as being constructed from pentamers and hexamers. The structures can be indexed by two integers ''h'' and ''k'', with <math>h \ge 1</math> and <math>k \ge 0</math>; the structure can be thought of as taking ''h'' steps from the edge of a pentamer, turning 60 degrees counterclockwise, then taking ''k'' steps to get to the next pentamer. The triangulation number ''T'' for the capsid is defined as:
:<math> T = h^2 + h \cdot k + k^2 </math>
In this scheme, icosahedral capsids contain 12 pentamers plus 10(''T''&nbsp;−&nbsp;1) hexamers.<ref>{{cite journal | vauthors = Carrillo-Tripp M, Shepherd CM, Borelli IA, Venkataraman S, Lander G, Natarajan P, Johnson JE, Brooks CL, Reddy VS | display-authors = 6 | title = VIPERdb2: an enhanced and web API enabled relational database for structural virology | journal = Nucleic Acids Research | volume = 37 | issue = Database issue | pages = D436-42 | date = January 2009 | pmid = 18981051 | pmc = 2686430 | doi = 10.1093/nar/gkn840 | url = http://viperdb.scripps.edu/virus.php | access-date = 2011-03-18 | archive-date = 2018-02-11 | archive-url = https://web.archive.org/web/20180211191026/http://viperdb.scripps.edu/virus.php | url-status = dead }}</ref><ref name="Johnson, J. E. and Speir, J.A. 2009 115–123">{{cite book | vauthors = Johnson JE, Speir JA |title=Desk Encyclopedia of General Virology|publisher=Academic Press |location=Boston |year=2009 |pages=115–123 |isbn=978-0-12-375146-1}}</ref> The ''T''-number is representative of the size and complexity of the capsids.<ref>{{cite journal | vauthors = Mannige RV, Brooks CL | title = Periodic table of virus capsids: implications for natural selection and design | journal = PLOS ONE | volume = 5 | issue = 3 | pages = e9423 | date = March 2010 | pmid = 20209096 | pmc = 2831995 | doi = 10.1371/journal.pone.0009423 | bibcode = 2010PLoSO...5.9423M | doi-access = free }}</ref> Geometric examples for many values of ''h'', ''k'', and ''T'' can be found at [[List of geodesic polyhedra and Goldberg polyhedra]].

Many exceptions to this rule exist: For example, the [[polyomavirus]]es and [[papillomaviruses]] have pentamers instead of hexamers in hexavalent positions on a quasi T = 7 lattice. Members of the double-stranded RNA virus lineage, including [[reovirus]], [[rotavirus]] and bacteriophage φ6 have capsids built of 120 copies of capsid protein, corresponding to a T = 2 capsid, or arguably a T = 1 capsid with a dimer in the asymmetric unit. Similarly, many small viruses have a pseudo T = 3 (or P = 3) capsid, which is organized according to a T = 3 lattice, but with distinct polypeptides occupying the three quasi-equivalent positions <ref>{{cite web | first = Jean-Yves | last = Sgro | work = Institute for Molecular Virology | publisher = University of Wisconsin-Madison | title=Virusworld | url=http://www.virology.wisc.edu/virusworld/tri_number.php }}</ref>