  In the course of investigating regular subalgebras of E(10) related to
cosmological solutions of 11-dimensional supergravity supporting an electric
4-form field, a class of rank 10 Coxeter subgroups of the Weyl group of E(10)
was uncovered (hep-th/0606123). These Coxeter groups all share the property
that their Coxeter graphs have incidence index 3, i.e. that each node is
incident to three and only three single lines. Furthermore, the Coxeter
exponents are either 2 or 3, but never infinity. We here go beyond subgroups of
the Weyl group of E(10) and classify all rank 10 Coxeter groups with these
properties. We find 21 distinct Coxeter groups of which 7 were already
described in hep-th/0606123. Moreover, we extend the classification to the rank
11 case and we find 252 inequivalent rank 11 Coxeter groups with incidence
index 4, of which at least 28 can be regularly embedded into E(11).
