  Can N-body simulations reliably determine the structural properties of dark
matter halos? Focussing on a Virgo-sized galaxy cluster, we increase the
resolution of current ``high resolution simulations'' by almost an order of
magnitude to examine the convergence of the important physical quantities. We
have 4 million particles within the cluster and force resolution 0.5 kpc/h
(0.05% of the virial radius). The central density profile has a logarithmic
slope of -1.5, as found in lower resolution studies of the same halo,
indicating that the profile has converged to the ``physical'' limit down to
scales of a few kpc. Also the abundance of substructure is consistent with that
derived from lower resolution runs; on the scales explored, the mass and
circular velocity functions are close to power laws of exponents ~ -1.9 and -4.
Overmerging appears to be globally unimportant for suhalos with circular
velocities > 100 km/s. We can trace most of the cluster progenitors from z=3 to
the present; the central object (the dark matter analog of a cD galaxy)is
assembled between z=3 and 1 from the merging of a dozen halos with v_circ \sim
300 km/s. The mean circular velocity of the subhalos decreases by ~ 20% over 5
billion years, due to tidal mass loss. The velocity dispersions of halos and
dark matter globally agree within 10%, but the halos are spatially anti-biased,
and, in the very central region of the cluster, they show positive velocity
bias; however, this effect appears to depend on numerical resolution.
