  Given an F-manifold one may construct a dual multiplication (generalizing the
idea of an almost-dual Frobenius manifold introduced by Dubrovin) using a
so-called eventual identity, the definition of which ensure that the dual
object is also an F-manifold. In this paper we solve the equations for an
eventual identity for a regular (so non-semi-simple) F-manifold and construct a
dual coordinate system in which dual multiplication is preserved. As an
application, families of Nijenhuis operators are constructed.
