  The usual propetry of s<-->t duality for scattering amplitudes, e.g. for
Veneziano amplitude, is deeply connected with the 2-dimensional geometry. In
particular, a simple geometric construction of such amplitudes was proposed in
a joint work by this author and S.Saito (solv-int/9812016). Here we propose
analogs of one of those amplitudes associated with multidimensional euclidean
spaces, paying most attention to the 3-dimensional case. Our results can be
regarded as a variant of "Regge calculus" intimately connected with ideas of
the theory of integrable models.
