  Inspired by the gauge/YBE correspondence this paper derives some
star-triangle type relations from dualities in $2d$ $\mathcal{N}=(0,2)$
$USp(2N)$ supersymmetric quiver gauge theories. To be precise, we study two
cases. The first case is the Intriligator-Pouliot duality in $2d$
$\mathcal{N}=(0,2)$ $USp(2N)$ theories. The description is performed explicitly
for $N=1,2,3,4,5$ and also for $N=3k+2$, which generalizes the situation in
$N=2,5$. For $N=1$ a triangle identity is obtained. For $N=2,5$ it is found
that the realization of duality implies slight variations of a star-triangle
relation type (STR type). The values $N=3,4$ are associated to a similar
version of the asymmetric STR. The second case is a new duality for $2d$
$\mathcal{N}=(0,2)$ $USp(2N)$ theories with matter in the antisymmetric tensor
representation that arises from dimensional reduction of $4d$ $\mathcal{N}=1$
$USp(2N)$ Cs\'aki-Skiba-Schmaltz duality. It is shown that this duality is
associated to a triangle type identity for any value of $N$. In all cases
Boltzmann weights as well as interaction and normalization factors are
completely determined. Finally, our relations are compared with those
previously reported in the literature.
