  The derivation of smooth cosmic billiard solutions through the compensator
method is extended to non maximal supergravities. A new key feature is the
non-maximal split nature of the scalar coset manifold. To deal with this, one
needs the theory of Tits Satake projections leading to maximal split projected
algebras. Interesting exact solutions that display several smooth bounces can
thus be derived. From the analysis of the Tits Satake projection emerges a
regular scheme for all non maximal supergravities and a challenging so far
unobserved structure, that of the paint group G-paint. This latter is preserved
through dimensional reduction and provides a powerful tool to codify solutions.
It appears that the dynamical walls on which the cosmic ball bounces come
actually in painted copies rotated into each other by G-paint. The effective
cosmic dynamics is that dictated by the maximal split Tits Satake manifold plus
paint. We work out in details the example provided by N=6,D=4 supergravity,
whose scalar manifold is the special Kahlerian SO*(12)}/SU(6)xU(1). In D=3 it
maps to the quaternionic E_7(-5)/ SO(12) x SO(3). From this example we extract
a scheme that holds for all supergravities with homogeneous scalar manifolds
and that we plan to generalize to generic special geometries. We also comment
on the merging of the Tits-Satake projection with the affine Kac--Moody
extensions originating in dimensional reduction to D=2 and D=1.
