  We continue our exercises with the universal $R$-matrix based on the
Khoroshkin and Tolstoy formula. Here we present our results for the case of the
twisted affine Kac--Moody Lie algebra of type $A^{(2)}_2$. Our interest in this
case is inspired by the fact that the Tzitz\'eica equation is associated with
$A^{(2)}_2$ in a similar way as the sine-Gordon equation is related to
$A^{(1)}_1$. The fundamental spin-chain Hamiltonian is constructed
systematically as the logarithmic derivative of the transfer matrix.
$L$-operators of two types are obtained by using q-deformed oscillators.
