  We construct and study polyhedral product models for classifying spaces of
right-angled Artin and Coxeter groups, general graph product groups and their
commutator subgroups. By way of application, we give a criterion of freeness
for the commutator subgroup of a graph product group, and provide an explicit
minimal set of generators for the commutator subgroup of a right-angled Coxeter
group.
