  Affine Toda field theories in two dimensions constitute families of
integrable, relativistically invariant field theories in correspondence with
the affine Kac-Moody algebras. The particles which are the quantum excitations
of the fields display interesting patterns in their masses and coupling and
which have recently been shown to extend to the classical soliton solutions
arising when the couplings are imaginary. Here these results are extended from
the untwisted to the twisted algebras. The new soliton solutions and their
masses are found by a folding procedure which can be applied to the affine
Kac-Moody algebras themselves to provide new insights into their structures.
The relevant foldings are related to inner automorphisms of the associated
finite dimensional Lie group which are calculated explicitly and related to
what is known as the twisted Coxeter element. The fact that the twisted affine
Kac-Moody algebras possess vertex operator constructions emerges naturally and
is relevant to the soliton solutions.
