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In this paper we discuss a relationship between the following two algebras:(i) the subconstituent algebra $T$ of a distance-regular graph that has$q$-Racah type; (ii) the $q$-tetrahedron algebra $\boxtimes_q$ which is a$q$-deformation of the three-point $sl_2$ loop algebra. Assuming that everyirreducible $T$-module is thin, we display an algebra homomorphism from$\boxtimes_q$ into $T$ and show that $T$ is generated by the image togetherwith the center $Z(T)$.

Distance-regular graphs of q-Racah type and the q-tetrahedron algebra