I originally asked basically this question on MSE here. From an appendix in Steinberg's "Conjugacy classes in algebraic groups" I found a list of the rational surface singularities. Equations of types $A_n, D_n, E_6, E_7$ and $E_8$ were given:
What I would like to do is construct (varieties isomorphic to) these as Toric varieties of a fan (as Fulton does it) or prove that it is not possible. As you can see from the link to my previous question, I know how to create the one of type $A_n$ but not the others. I suspect it is not possible but I don't know how to prove that. Can anyone help me resolve this?
Thank you very much.
Sorry, my list is different to Steinberg's, I can't remember where my incorrect list is from then. Steinberg's list: