The hypercube is a generalization of 3-cube to n dimensions, also called an n-cube or measure polytope. In this paper we define boundary edNCE recursive graph grammar and generate the language for the hypercube. For a graph grammar G with a graph-theoretical property, let be the language L(G) squeezed with i.e., This paper presents result on language-theoretic properties (such as membership and other decision properties) of NLC, B-edNCE languages squeezed with hyper cube graphs. We show that is in NP complete.