Repr\'esentations de r\'eflexion de groupes de Coxeter Sixi\`eme partie: le cas r\'eductible; exemples en rang trois

In this sixth part we study rank $3$ reflection groups not well generated: $G(2r,r,2)$, $G_{12}$, $G_{13}$ and $G_{22}$. We start from a reflection representation of a rank $3$ Coxeter group and we show that we can obtain in this manner affine Coxeter groups whose linear part is one of the preceding groups.