  We present the design of a mesh quality indicator that can predict the
behavior of the Virtual Element Method (VEM) on a given mesh family or finite
sequence of polyhedral meshes (dataset). The mesh quality indicator is designed
to measure the violation of the mesh regularity assumptions that are normally
considered in the convergence analysis. We investigate the behavior of this new
mathematical tool on the lowest-order conforming approximation of the
three-dimensional Poisson equation. This work also assesses the convergence
rate of the VEM when applied to very general polyhedral meshes, including
non-convex and skewed three-dimensional elements. Such meshes are created
within an original mesh generation framework, which is designed to allow the
generation of meshes with very different sizes, connectivity and geometrical
properties. The obtained results show a significant correlation between the
quality measured a priori by the indicator and the effective performance of the
VEM.
