  We construct a geometric model for the root category $\mathcal{D}^b(Q)/[2]$
of any Dynkin diagram $Q$, which is an $h_Q$-gon $\mathbf{V}_Q$ with cores,
where $h_Q$ is the Coxeter number and $\mathcal{D}^b(Q)$ is the bounded derived
category associated to $Q$. As an application, we classify all spaces
$\mathrm{ToSt}\mathcal{D}$ of total stability conditions on triangulated
categories $\mathcal{D}$, where $\mathcal{D}$ must be of the form
$\mathcal{D}^b(Q)$. More precisely, we prove that
$\mathrm{ToSt}\mathcal{D}^b(Q)/[2]$ is isomorphic to a suitable moduli space of
stable $h_Q$-gons of type $Q$.
  In particular, an $h_Q$-gon $\mathbf{V}$ of type $D_n$ is a (centrally)
symmetric doubly punctured $2(n-1)$-gon. $\mathbf{V}$ is stable if it is convex
and the punctures are inside the level-$(n-2)$ diagonal-gon. Another
interesting case is $E_6$, where the (stable) $h_Q$-gon (dodecagon) can be
realized as a pair of planar tiling pattern.
