  Faddeev' equations are a set-theoretical and an operator forms of the
star-triangle equation. Known solutions of the quantum star-triangle equation,
related to the Faddeev equations, are based on various forms of the modular
double of the Weyl algebra including its cyclic representation. We show in this
paper that Fadeev's equation also leads to a solution of the quantum
star-triangle equation even in the case of a simple Weyl algebra with $|q|<1$.
This paper can be seen as an addendum to the recent paper "V. Bazhanov and S.
Sergeev, A distant descendant of the six-vertex model, arXiv:2310.08427".
