Triangulation numbers and Constraints.

<p>The standard Triangulation number architecture for spherical capsids ranging from T1 to T7 capsids. Each are composed of 12 pentamers (5-protein units) and a variable number of hexamers (6-protein units). The Asymmetric Unit (AU) for each capsid is shown as a red kite stretching from the 5-fold (blue pentagon) to each of the 2-folds (red diamonds) to the 3-fold axes (green triangle). The icosahedral great circles also encompass each of the 5 distinct red lines shown. As the triangulation number increases, the hexamers must rearrange as seen, which changes the restrictions on their protrusions, shown as dashed lines above. While the capsid proteins are considered to be quasi-equivalent, they are not for the purpose of protrusions. The dotted lines show where modifications for bioengineering will likely be less favorable, except where they intersect with the boundaries of the AU (<i>i.e</i>. the great circles). In general it also appears the p23 within the AU is less favorable. The icosahedral capsids were drawn using the Icosahedral Server [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0152319#pone.0152319.ref003" target="_blank">3</a>].