  We construct new solvable vertex models based on the spin representation of
the Lie algebra $B_k$. We use these models to study the algebraic structure
underlying such vertex theories. We show that all the $B_k$ spin vertex models
obey a version of the BMW algebra along with extra relations that are called
$n$--CB (conformal braiding) algebras. These algebras were discussed before for
various IRF (interaction round the face) models. Here we establish that the
same algebras hold for vertex models.
