On the resolution of singularities in affine toric 3- varieties

Let $x_{Sigma(sigma)}= {rm spec C[check sigma cap Z}^{n}]$ be an affine toric variety given by the monoid algebra $rm C[check sigma cap Z^{n}]$ , $check sigma$ the negative dual cone of a lattice cone σ ? Rⁿ, Σ(σ) the fan consisting of the faces of σ. Assume XΣ(σ) to have only quotient singularities. For n = 3 we classify all pairs X_Σ′, X_Σ(σ) which occur in minimal models of equivariant resolutions Φ: X_Σ′ → - X_Σ(σ) sucn that the regular toric variety XΣ′ has Picard number at most 3.