  We develop a numerical assessment of the Virtual Element Method for the
discretization of a diffusion-reaction model problem, for higher "polynomial"
order k and three space dimensions. Although the main focus of the present
study is to illustrate some h-convergence tests for different orders k, we also
hint on other interesting aspects such as structured polyhedral Voronoi
meshing, robustness in the presence of irregular grids, sensibility to the
stabilization parameter and convergence with respect to the order k.
