  The present paper has two objectives. On one side, we develop and test
numerically divergence free Virtual Elements in three dimensions, for variable
``polynomial'' order. These are the natural extension of the two-dimensional
divergence free VEM elements, with some modification that allows for a better
computational efficiency. We test the element's performance both for the Stokes
and (diffusion dominated) Navier-Stokes equation.
  The second, and perhaps main, motivation is to show that our scheme, also in
three dimensions, enjoys an underlying discrete Stokes complex structure. We
build a pair of virtual discrete spaces based on general polytopal partitions,
the first one being scalar and the second one being vector valued, such that
when coupled with our velocity and pressure spaces, yield a discrete Stokes
complex.
