$A_1$ (aka The Cone) $x^2+y^2-z^2=0$
 $A_1$ in different coordinates $z^2+x^2-y^2=0$
 $A_2$ (aka The Cusp) $z^2+y^2+x^3=0$
 $A_4$ $z^2+y^2+x^5=0$
 $A_6$ $z^2+y^2+x^7=0$
 $A_3$ $z^2+y^2-x^4=0$
 $A_5$ $z^2+y^2-x^6=0$
 $A_7$ $z^2+y^2-x^8=0$
 $D_4$ $z^2+x(y^2-x^2)=0$
 $D_6$ $z^2+x(y^2-x^4)=0$
 $D_8$ $z^2+x(y^2-x^6)=0$
 $D_5$ $z^2+x(y^2-x^3)=0$
 $D_7$ $z^2+x(y^2-x^5)=0$
 $D_9$ $z^2+x(y^2-x^7)=0$
 $E_6$ $z^2+x^3+y^4=0$
 $E_7$ $z^2+x(x^2+y^3)=0$
 $E_8$ $z^2+x^3+y^5=0$

*: Real pictures of some complex quotient singularities $\mathbb{C}^2 / \Gamma$, where $\Gamma$ is a finite subgroup of $SL_2(\mathbb{C})$. These surfaces are also known as ADE surfaces or Kleinian surfaces or $2$-dimensional rational double points or ...
In each surface a curve is highlighted. This curve is the intersection of the surface with the plane $\{ z =0 \}$, or, if we stay in the context of groups, it is the discriminant curve of the complex reflection group $G$ such that $[G:\Gamma]=2$, that is, $\Gamma=G \cap SL_2(\mathbb{C})$.