“…For example, models based on energy minimisation, and consequently the techniques of the vectorial Calculus of Variations, have been very successful in materials science where typical specimens are polyhedral. Indeed, the work presented here has been largely motivated by [5] where, in a simplified model, a set of quasiconvexity conditions at edges and corners of a (convex) polyhedral domain was employed to explain remarkable experimental observations in a shape-memory alloy (see [6]). In particular, it was shown that, in this simplified model, the quasiconvexity conditions hold in the interior and at edges, thus preventing the localised nucleation of the high temperature phase; in contrast, and consistent with observations, quasiconvexity was lost at certain corners allowing for nucleation.…”