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Several studies have proposed that the shape of the Universe may be aPoincare dodecahedral space (PDS) rather than an infinite, simply connected,flat space. Both models assume a close to flat FLRW metric of about 30% matterdensity. We study two predictions of the PDS model. (i) For the correct model,the spatial two-point cross-correlation function, $\ximc$, of temperaturefluctuations in the covering space, where the two points in any pair are ondifferent copies of the surface of last scattering (SLS), should be of asimilar order of magnitude to the auto-correlation function, $\xisc$, on asingle copy of the SLS. (ii) The optimal orientation and identified circleradius for a "generalised" PDS model of arbitrary twist $\phi$, found bymaximising $\ximc$ relative to $\xisc$ in the WMAP maps, should yield $\phi \in\{\pm 36\deg\}$. We optimise the cross-correlation at scales < 4.0 h^-1 Gpcusing a Markov chain Monte Carlo (MCMC) method over orientation, circle sizeand $\phi$. Both predictions were satisfied: (i) an optimal "generalised" PDSsolution was found, with a strong cross-correlation between points which wouldbe distant and only weakly correlated according to the simply connectedhypothesis, for two different foreground-reduced versions of the WMAP 3-yearall-sky map, both with and without the kp2 Galaxy mask: the face centres are$(l,b)_{i=1,6}\approx (184d, 62d), (305d, 44d), (46d, 49d), (117d, 20d), (176d,-4d), (240d, 13d) to within ~2d, and their antipodes; (ii) this solution hastwist \phi= (+39 \pm 2.5)d, in agreement with the PDS model. The chance of thisoccurring in the simply connected model, assuming a uniform distribution $\phi\in [0,2\pi]$, is about 6-9%.

The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps