  The aim of this paper is to define and study some quasi-hereditary covers for
higher zigzag algebras. We will show how these algebras satisfy three different
Koszul properties: they are Koszul in the classical sense, standard Koszul and
Koszul with respect to the standard module $\Delta$, according with the
definition given in \cite{Madsen1}. This last property gives rise to a well
defined duality and the $\Delta$-Koszul dual will be computed as the path
algebra of a quiver with relations.
