  In this study, we propose a virtual element scheme to solve the Darcy problem
in three physical dimensions. The main novelty, here proposed, is that curved
elements are naturally handled without any degradation of the solution
accuracy. In fact, in presence of curved boundaries, or internal interfaces,
the geometrical error introduced by planar approximations may dominate the
convergence rate limiting the benefit of high-order approximations. We consider
the Darcy problem in its mixed form to directly obtain, with our numerical
scheme, accurate and mass conservative fluxes without any post-processing. An
important step to derive this new scheme is the actual computation of
polynomials over curved polyhedrons, here presented and discussed. Finally, we
show the theoretical analysis of the scheme as well as several numerical
examples to support our findings
