  This is the second in a series of papers which give an explicit description
of the reconstruction algebra as a quiver with relations; these algebras arise
naturally as geometric generalizations of preprojective algebras of extended
Dynkin diagrams. This paper deals with dihedral groups G=D_{n,q} for which all
special CM modules have rank one, and we show that all but four of the
relations on such a reconstruction algebra are given simply as the relations
arising from a reconstruction algebra of type A. As a corollary, the
reconstruction algebra reduces the problem of explicitly understanding the
minimal resolution (=G-Hilb) to the same level of difficulty as the toric case.
