Abstract
A class of expandable polyhedral structures, the expandohedra, consisting of prismatic faces linked along edges by hinged plates, provides a model for the swelling of viruses. The finite breathing mode of the expandohedra, apparent in the model, and from geometric arguments, is not, however, detected by elementary counting techniques. Symmetry extended mobility criteria show that the breathing motion is part of a set of face mechanisms for many expandohedra. Numerical analysis using the singular value decomposition of the compatibility matrix confirms the completeness of the deductions from general symmetry theorems, derived for expandohedra.
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