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Double-link expandohedra: a mechanical model for expansion of a virus. (English) Zbl 1063.92030
Summary: Double-link expandohedra are introduced: each is constructed from a parent polyhedron by replacing all faces with rigid plates, adjacent plates being connected by a pair of spherically jointed bars. Powerful symmetry techniques are developed for mobility analysis of general double-link expandohedra, and when combined with numerical calculation and physical model building, they demonstrate the existence of generic finite breathing expansion motions in many cases. For icosahedrally symmetric trivalent parents with pentagonal and hexagonal faces only (fullerene polyhedra), the derived expandohedra provide a mechanical model for the experimentally observed swelling of viruses such as cowpea chlorotic mottle virus (CCMV). A fully symmetric swelling motion (a finite mechanism) is found for systems based on icosahedral fullerene polyhedra with odd triangulation number, $$T\leq 31$$, and is conjectured to exist for all odd triangulation numbers.

##### MSC:
 92C50 Medical applications (general) 92C40 Biochemistry, molecular biology 92C10 Biomechanics 74L15 Biomechanical solid mechanics
##### Keywords:
polyhedra; virus structures; symmetry groups
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