  We introduce the notion of coupled link cube complex (CLCC) as a means of
constructing interesting cocompactly cubulated groups. CLCCs are defined
locally, making them a useful tool when precise control over the links is
required. In this paper we study some general properties of CLCCs, such as
their (co)homological dimension and criteria for hyperbolicity. Some examples
of fundamental groups of CLCCs are RAAGs, RACGs, surface groups and some
manifold groups. As immediate applications of our criteria we produce a number
of cubulated 3 and 4 manifolds with hyperbolic fundamental group.
