  We introduce quasi-hereditary endomorphism algebras defined over a new class
of finite dimensional monomial algebras with a special ideal structure. The
main result is a uniform formula describing the Ringel duals of these
quasi-hereditary algebras.
  As special cases, we obtain a Ringel-duality formula for a family of strongly
quasi-hereditary algebras arising from a type A configuration of projective
lines in a rational, projective surface as recently introduced by Hille and
Ploog, for certain Auslander-Dlab-Ringel algebras, and for Eiriksson and
Sauter's nilpotent quiver algebras when the quiver has no sinks and no sources.
We also recover Tan's result that the Auslander algebras of self-injective
Nakayama algebras are Ringel self-dual.
