Orbifold del Pezzo Surfaces in ℙ¹ × ℙ¹ × 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 (Formula presented.). We construct such models of del Pezzo surface with embeddings in (Formula presented.) 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 (Formula presented.) in (Formula presented.); giving rise to codimension 4 Gorenstein varieties. We also compute a formula for the Hilbert series of a general weighted (Formula presented.) variety that plays a pivotal role in these constructions.