  In this paper the three-dimensional vertex model is given, which is the
duality of the three-dimensional Baxter-Bazhanov (BB) model. The braid group
corresponding to Frenkel-Moore equation is constructed and the transformations
$R, I$ are found. These maps act on the group and denote the rotations of the
braids through the angles $\pi$ about some special axes. The weight function of
another three-dimensional vertex model related the 3D lattice integrable model
proposed by Boos, Mangazeev, Sergeev and Stroganov is presented also, which can
be interpreted as the deformation of the vertex model corresponding to the BB
model.
