Can the group generated by local complementations, ${lc_i|i=1,\cdots,n}$ on simple graphs on $n$ vertices, be categorized as a coxeter group? After all these obey: \begin{equation} \langle lc_i| (lc_i lc_j)^{m_{ij}}=1\rangle \quad where \quad m_{ij}=\{ 2,3,6\} \end{equation}

If so, which classification do they belong to?