  We investigate numerically the phase structure of the Twisted Eguchi-Kawai
(TEK) model in four dimensions. In the numerical simulations of the zero
temperature TEK model (using a symmetric twist) we observe the existence of new
phases that break its centre symmetry at intermediate lattice couplings and for
large SU(N) gauge groups. This effect can be explained by the contribution of
diagonal configurations with collapsed eigenvalues, which are particular cases
of ``generalised fluxons''. We also investigate finite temperature versions of
the TEK model using anisotropic lattice couplings, where in particular we find
van Baal fluxons contributing at large anisotropies.
