  We consider graded twisted Calabi-Yau algebras of dimension 3 which are
derivation-quotient algebras of the form $A = \kk Q/I$, where $Q$ is a quiver
and $I$ is an ideal of relations coming from taking partial derivatives of a
twisted superpotential on $Q$. We define the type $(M, P, d)$ of such an
algebra $A$, where $M$ is the incidence matrix of the quiver, $P$ is the
permutation matrix giving the action of the Nakayama automorphism of $A$ on the
vertices of the quiver, and $d$ is the degree of the superpotential. We study
the question of what possible types can occur under the additional assumption
that $A$ has polynomial growth. In particular, we are able to give a nearly
complete answer to this question when $Q$ has at most 3 vertices.
