Consider the toric surface corresponding to the fan $\Delta$ consisting of $$\sigma_1=\langle e_1,-e_1+2e_2\rangle$$ $$\sigma_2=\langle-e_1+2e_2,-e_1-2e_2\rangle$$ $$\sigma_3=\langle -e_1-2_2,e_1\rangle$$ and their faces.
Since the fan is simplicial, the toric variety is a simplicial toric variety. So it has singularities. However I am unable to identify what the singular points are.
For example if I just take the cone $\sigma_1$, the corresponding affine toric variety has a singularity at the origin. But how do I find the singular points of the toric variety corresponding to $\Delta$?