Consider a Coxeter group presentation $< s_1, \ldots s_n \mid (s_i s_j)^{m_{ij}}>$ with $m_{ii}=1$ for all $i$. I can prove (using http://arxiv.org/abs/1011.4255) that if for each $i$ there are at most two $j\neq i$ with $m_{ij}< \infty$, then the corresponding Cayley graph is planar. Is this fact known?

In fact I can do a bit more, namely prove that by defining two 2-cells of the cayley complex to be parallel if they have the same boundary, and deleting all but one 2-cells from each parallel class, we obtain a planar 2-complex. This might be interesting as it gives a nice action of the group on the 2-sphere.