  Dimensional reduction of (super-)gravity theories to 3 dimensions results in
sigma models on coset spaces G/H, such as the E_8/SO(16) coset in the bosonic
sector of 3 dimensional maximal supergravity. The reverse process, oxidation,
is the reconstruction of a higher dimensional gravity theory from a coset sigma
model. Using the group G as starting point, the higher dimensional models
follow essentially from decomposition into subgroups. All equations of motion
and Bianchi identities can be directly reconstructed from the group lattice,
Kaluza-Klein modifications and Chern-Simons terms are encoded in the group
structure. Manipulations of extended Dynkin diagrams encode matter content, and
(string) dualities. The reflection symmetry of the ``magic triangle'' for E_n
gravities, and approximate reflection symmetry of the older ``magic triangle''
of supergravities in 4 dimensions, are easily understood in this framework.
