  We show that every graph product of finitely generated abelian groups acts
properly and cocompactly on a CAT(0) cubical complex. The complex generalizes
(up to subdivision) the Salvetti complex of a right-angled Artin group and the
Coxeter complex of a right-angled Coxeter group. In the right-angled Artin
group case it is related to the embedding into a right-angled Coxeter group
described by Davis and Januszkiewicz. We compare the approaches and also adapt
the argument that the action extends to finite index supergroup that is a graph
product of finite groups.
