  In this paper, we continue the study of intersections of closed curves on
translation surfaces, initiated in by S. Cheboui, A. Kessi and D. Massart for a
family of arithmetic Veech surfaces and the author, E. Lanneau and D. Massart
for a family of non-arithmetic Veech surfaces. Namely, we investigate the
question of maximizing the algebraic intersection between two curves of given
lengths by studying the quantity KVol defined for any closed orientable surface
by:
  $$ \mathrm{KVol}(X): = \mathrm{Vol}(X,g)\cdot \sup_{\alpha,\beta}
\frac{\mathrm{Int} (\alpha,\beta)}{l_g (\alpha) l_g (\beta)},$$ where the
supremum is taken over all pairs of closed curves on $X$. In this paper we
focus on regular $n$-gons for even $n \geq 8$ as well as their Teichm\"uller
disks.
