  In this paper we study dynamical compactification in Einstein-Gauss-Bonnet
gravity from arbitrary dimension for generic values of the coupling constants.
We showed that, when the curvature of the extra dimensional space is negative,
for any value of the spatial curvature of the four dimensional space-time one
obtains a realistic behavior in which for asymptotic time both the volume of
the extra dimension and expansion rate of the four dimensional space-time tend
to a constant. Remarkably, this scenario appears within the open region of
parameters space for which the theory does not admit any maximally symmetric
(4+D)- dimensional solution, which gives to the dynamical compactification an
interpretation as geometric frustration. In particular there is no need to
fine-tune the coupling constants of the theory so that the present scenario
does not violate "naturalness hypothesis". Moreover we showed that with
increase of the number of extra dimensions the stability properties of the
solution are increased.
