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We determine restrictions on the singularity content of a Fano polygon, orequivalently of certain orbifold del Pezzo surfaces. We establish bounds on themaximum number of 1/R(1,1) singularities in the basket of residualsingularities. In particular, there are no Fano polygons withoutT-singularities and with a basket given by (i) {k x 1/R(1,1)} where k is apositive integer and R>4, or (ii) {1/R1(1,1), 1/R2(1,1), 1/R3(1,1)}.

Restrictions on the Singularity Content of a Fano Polygon