  In this paper we show that acyclic $n$-slice algebras are exactly acyclic
$n$-hereditary algebras whose $(n+1)$-preprojective algebras are
$(q+1,n+1)$-Koszul. We also list the equivalent triangulated categories arising
from the algebra constructions related to an $n$-slice algebra. We show that
higher slice algebras of finite type appear in pairs and they share the
Auslander-Reiten quiver for their higher preprojective components.
