  The full three-year WMAP results (WMAP3) reinforce the absence of large-angle
correlations at scales greater than 60 degrees. The Poincare dodecahedral space
(PDS) model model, which may naturally explain such features, thus remains a
plausible cosmological model, despite recent controversy about whether matched
circle searches would or would not push the topology beyond the horizon. Here,
we have used new eigenmode calculations of the dodecahedral space to predict
the cosmic microwave background (CMB) temperature fluctuations in such models,
with an improved angular resolution. We have simulated CMB maps and confirmed
the expected presence of matching circles. For a set of plausible cosmological
parameters, we have derived the angular power spectrum of the CMB up to large
wavenumbers. Comparison with the WMAP3 observations confirms a remarkable fit
with a PDS model, for a value $\Omega_0 = 1.018$ of the average total energy
density.
