Polynomials from the closure of the principal hyperbolic domain of the cubic connectedness locus have some specific properties, which were studied in a recent paper by the authors. The family of (affne conjugacy classes of) all polynomials with these properties is called the Main Cubioid. In this paper, we describe a combinatorial counterpart of the Main Cubioid | the set of invariant laminations that can be associated to polynomials from the Main Cubioid.