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Computational and Mathematical Methods in Medicine
Volume 9, Issue 3-4, Pages 295-302
Original Article

The Influence of Symmetry on the Probability of Assembly Pathways for Icosahedral Viral Shells

1Department of Mathematics, University of Florida, Gainesville, FL, USA
2CISE Department, University of Florida, Gainesville, FL, USA

Received 19 March 2008; Accepted 7 May 2008

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper motivates and sets up the mathematical framework for a new program of investigation: to isolate and clarify the precise influence of symmetry on the probability space of assembly pathways that successfully lead to icosahedral viral shells. Several tractable open questions are posed. Besides its virology motivation, the topic is of independent mathematical interest for studying constructions of symmetric polyhedra. Preliminary results are presented: a natural, structural classification of subsets of facets of T = 1 polyhedra, based on their stabilizing subgroups of the icosahedral group; and a theorem that uses symmetry to formalize why increasing depth increases the numeracy (and hence probability) of an assembly pathway type (or symmetry class) for a T = 1 viral shell.