Dimers for Relativistic Toda Models with Reflective Boundaries

We construct dimer graphs for relativistic Toda chains associated with classical untwisted Lie algebras of A, B, C${}_0$, C${}_{\pi }$, D types and twisted A, D types. We show that the Seiberg-Witten curve of 5d $\mathcal{N}=1$ pure supersymmetric gauge theory of gauge group $G$ is a spectral curve of the relativistic Toda chain of the dual group $G^{\vee }$.