Toric surfaces glued from affine plane $\mathbb{A}^2$'s

Question

I'm figuring out toric surfaces corresponding to the following six toric fans in $\mathbb{R}^2$.

I found that the first one corresponds to the affine plane $\mathbb{A}^2$, and the second one corresponds to the blown up surface $\mathcal{O}_{\mathbb{P}^1}(-1)$.

But I couldn't find a nice description of the other four surfaces. Do they also have a good name or some nice understanding?