  In this paper, we show that the $n$-APR tilts of dual $\tau$-slice algebras
of acyclic stable $n$-translation algebras are realized as $\tau$-mutations.
Such dual $\tau$-slice algebras are quasi $(n-1)$-Fano when the $n$-translation
algebra is Koszul, and a recursive construction of higher quasi Fano algebras
for quasi $n$-Fano algebra obtained in this way is given. The $\tau_n$-closure
and $\nu_n$-closure of such algebras are studied and we show that for an
acyclic dual $n$-translation algebras with bound quiver $Q^{\perp}$, the
Auslander-Reiten quivers of its $\tau_n$-closures are truncation of the quiver
$\mathbb{Z}|_n Q^{\perp}$, and the Auslander-Reiten quiver of its
$\nu_n$-closure is $\mathbb{Z}|_n Q^{\perp}$ when it is $n$-representation
infinite.
