  The notion of a $(k,n)$-frieze pattern was introduced by the author as a
generalisation of the classical frieze patterns. In this article we describe
connections between classes of $(3,n)$-frieze patterns and classes of
$\mathrm{SL}_3$-frieze patterns. We introduce the idea of a superimposed
triangulation and clarify how superimposed triangulations may be used to
understand quiddity sequences for $\mathrm{SL}_3$-frieze patterns.
