In this paper, we present a three-dimensional discrete model governing the deformation of a viral capsid, modelled as a regular icosahedron and subjected not to cross a given flat rigid surface on which it initially lies in correspondence of one vertex only. First, we set up the model in the form of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable space. Second, we show the existence and uniqueness of the solution for the proposed model. Third, we numerically test this model and we observe that the outputs of the numerical experiments comply with physics. Finally, we establish the existence of solutions for the corresponding time-dependent version of the obstacle problem under consideration.

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