  In a recent paper, Doran, Greene and Judes considered one parameter families
of quintic threefolds with finite symmetry groups. A surprising result was that
each of these six families has the same Picard Fuchs equation associated to the
holomorphic 3-form. In this paper we give an easy argument, involving the
family of Mirror Quintics, which implies this result. Using a construction due
to Shioda, we also relate certain quotients of these one parameter families to
the family of Mirror Quintics. Our constructions generalize to degree n Calabi
Yau varieties in (n-1)-dimensional projective space.
