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A new counting polynomial, called Omega Ω(G,x), was recently proposed by Diudea. It is defined on the ground of “opposite edge strips” ops. Two related polynomials: Sadhana Sd(G,x) and Theta Θ(G,x)  polynomials can also be calculated by ops counting. Close formulas for calculating these three polynomials in infinite nano-structures resulted by embedding the titanium dioxide pattern in plane, cylinder and torus are derived. For the design of titanium dioxide pattern, a procedure based on a sequence of map operations is proposed.

Keywords: Titanium oxide, Omega polynomial, Sadhana polynomial, Theta polynomial