  We study the N = 2 gauge theories obtained by engineering the Type IIB
superstring on the quasi-homogeneous elements of Arnold's list of bimodal
singularities. All these theories have finite BPS chambers and we describe,
along the lines of [arXiv:1107.5747], the algebraically obvious ones.
  Our results leads to the prediction of 11 new periodic Y-systems, providing
additional evidence for the correspondence in between thermodinamical Bethe
ansatz periodic Y-systems and N = 2 superconformal theories with a finite BPS
chamber whose chiral primaries have dimensions of the form $\mathbb{N}/\ell$.
