  Let $\Gamma$ denote a distance-regular graph with classical parameters
$(D,b,\alpha,\beta)$ and $b\not=1$, $\alpha=b-1$. The condition on $\alpha$
implies that $\Gamma$ is formally self-dual. For $b=q^2$ we use the adjacency
matrix and dual adjacency matrix to obtain an action of the $q$-tetrahedron
algebra $\boxtimes_q$ on the standard module of $\Gamma$. We describe four
algebra homomorphisms into $\boxtimes_q$ from the quantum affine algebra
$U_q({\hat{\mathfrak{sl}}_2})$; using these we pull back the above
$\boxtimes_q$-action to obtain four actions of $U_q({\hat{\mathfrak{sl}}_2})$
on the standard module of $\Gamma$.
