Darboux transformations with tetrahedral reduction group and related   integrable systems
  In this paper we derive new two-component integrable differential difference and partial difference systems by applying a Lax-Darboux scheme to an operator formed from an ${\mathfrak{sl}}_3({\mathbb{C}})$-based automorphic Lie algebra. The integrability of the found systems is demonstrated via Lax pairs and generalised symmetries. 
George Berkeley, Alexander V. Mikhailov and Pavlos Xenitidis
nlin.SI