  We use F. Ferrari's methods relating matrix models to Calabi-Yau spaces in
order to explain much of Intriligator and Wecht's ADE classification of $\N=1$
superconformal theories which arise as RG fixed points of $\N = 1$ SQCD
theories with adjoints. We find that ADE superpotentials in the
Intriligator-Wecht classification exactly match matrix model superpotentials
obtained from Calabi-Yaus with corresponding ADE singularities. Moreover, in
the additional $\Hat{O}, \Hat{A}, \Hat{D}$ and $\Hat{E}$ cases we find new
singular geometries. These `hat' geometries are closely related to their ADE
counterparts, but feature non-isolated singularities. As a byproduct, we give
simple descriptions for small resolutions of Gorenstein threefold singularities
in terms of transition functions between just two coordinate charts. To obtain
these results, we develop an algorithm for blowing down exceptional $\PP^1$s,
described in the appendix.
