Orbifold del Pezzo Surfaces in P1 x P1 x P1 Format

We introduce the notion of biregular index models (infinite series) of orbifold del Pezzo surfaces having their (sub) anti-canonical embeddings in some weighted projective space P(w(i)). We construct such models of del Pezzo surface with embeddings in P-6(wi) containing at worst rigid orbifold points. The equations describing their images under their (sub) anti-canonical embeddings can be computed by using equations of the Segre embedding of P-1 x P-1 x P-1 in P-7; giving rise to codimension 4 Gorenstein varieties. We also compute a formula for the Hilbert series of a general weighted P-1 x P-1 x P-1 -> P-7(w(i)) variety that plays a pivotal role in these constructions.