We re-examine previously found cosmological solutions to eleven-dimensional supergravity in the light of the E_{ 10}-approach to M-theory. We focus on the solutions with non zero electric field determined by geometric configurations (n_m, g_3), n\leq 10. We show that these solutions are associated with rank $g$ regular subalgebras of E_{ 10}, the Dynkin diagrams of which are the (line) incidence diagrams of the geometric configurations. Our analysis provides as a byproduct an interesting class of rank-10 Coxeter subgroups of the Weyl group of E_{ 10}.
Categories: hep-th gr-qc math.GR