  We introduce a new quasi-isometry invariant of 2-dimensional right-angled
Coxeter groups, the hypergraph index, that partitions these groups into
infinitely many quasi-isometry classes, each containing infinitely many groups.
Furthermore, the hypergraph index of any right-angled Coxeter group can be
directly computed from the group's defining graph. The hypergraph index yields
an upper bound for a right-angled Coxeter group's order of thickness, order of
algebraic thickness and divergence function. Finally, given an integer n>1, we
give examples of right-angled Coxeter groups which are thick of order n, yet
are algebraically thick of order strictly larger than n, answering a question
of Behrstock-Drutu-Mosher.
