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We construct two types of wellformed and quasismooth biregular models(infinite series) of rigid orbifold del Pezzo surfaces having their (sub)anti-canonical embeddings in $\mathbb P^6(w_i) $. One type of model contains afamily of rigid del Pezzo surfaces with a fixed Fano index and weights ofambient $\mathbb P^6(w_i)$ are parameterized by positive integers. In the othertype of models, weights of $\mathbb P^6(w_i)$ and Fano index, both areparameterized by the positive integers. The equations describing their imagesunder (sub) anti-canonical embeddings are given in terms of the equations ofthe Segre embedding of $\mathbb P^1 \times \mathbb P^1\times \mathbb P^1$,which has codimension 4 in $\mathbb P^7$. We also give a formula for theHilbert series of a generic weighted $\mathbb P^1 \times \mathbb P^1\times\mathbb P^1$ variety, a key tool in these constructions.

Obrifold del Pezzo surfaces in $\mathbb P^1 \times \mathbb P^1\times \mathbb P^1$ format