  Exact spectra of periodic samples are computed up to $ N=36 $.
  Evidence of an extensive set of low lying levels, lower than the softest
magnons, is exhibited.
  These low lying quantum states are degenerated in the thermodynamic limit;
their symmetries and dynamics as well as their finite-size scaling are strong
arguments in favor of N\'eel order.
  It is shown that the N\'eel order parameter agrees with first-order spin-wave
calculations. A simple explanation of the low energy dynamics is given as well
as the numerical determinations of the energies, order parameter and spin
susceptibilities of the studied samples. It is shown how suitable boundary
conditions, which do not frustrate N\'eel order, allow the study of samples
with $ N=3p+1 $ spins.
  A thorough study of these situations is done in parallel with the more
conventional case $ N=3p $.
