  In this paper, we describe a general setting for dimer models on cylinders
over Dynkin diagrams which in type A reduces to the well studied case of dimer
models on a disc. We prove that all Berenstein--Fomin--Zelevinsky quivers for
Schubert cells in a symmetric Kac--Moody algebra give rise to dimer models on
the cylinder over the corresponding Dynkin diagram. We also give an independent
proof of a result of Buan, Iyama, Reiten and Smith that the corresponding
superpotentials are rigid using the dimer model structure of the quivers.
