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In this third part, we make the following hypothesis: representation$R=R(\alpha,\beta,\gamma ;l)$ of $W(p,q,r)$ is reducible and there exist a$G$-invariant non-nulle bilinear form where $G=Im R$. With those conditions, weknow the structure of $G$: $G'=G/N(G)$ is isomorphic to a finite dihedral groupand $N(G)$ is given explicitly as well as the action of $G$ on $N(G)$. We beginby giving conditions on $p,q,r$ as well on $\alpha,\beta,\gamma$ and we proovethem in the appendix. The general case will be studied in the next part.

Repr\'esentations de r\'eflexion de groupes de Coxeter -- Troisi\`eme partie: les groupes di\'edraux affines