  We propose a geometric explanation of the standard model of Glashow, Weinberg
and Salam for the known elementary particles. Our model is a generic Quantum
Field Theory in dimension four, obtained by developing along a Lorentz
sub-manifold the lagrangian of Einstein and Dirac in dimension twelve. The main
mechanism which gives birth to the standard model is a certain gauge fixing of
triality, which permits to identify the multiplicity of fermions, as seen from
the four dimensional world, with the eight unseen dimensions of the generating
universe. In this way we get the known tables of particles, explaining the
series of fermions and the gauge bosons. We suggest that the Higgs field
dynamics could appear through a bosonization of the right handed neutrino and
correspond to a displacement in the unseen dimensions. We also propose
hypotheses for dark matter, and perhaps dark energy. Then we suggest
predictions to go beyond the standard model.
