  Frieze patterns of integers were studied by Conway and Coxeter. Let
$\mathscr{C}$ be the cluster category of Dynkin type $A_n$. Indecomposables in
$\mathscr{C}$ correspond to diagonals in an $(n+3)$-gon. Work done by Caldero
and Chapoton showed that the Caldero-Chapoton map (which is a map dependent on
a fixed object $R$ of a category, and which goes from the set of objects of
that category to $\mathbb{Z}$), when applied to the objects of $\mathscr{C}$
can recover these friezes. This happens precisely when $R$ corresponds to a
triangulation of the $(n+3)$-gon. Later work by authors such as Bessenrodt,
Holm, Jorgensen and Rubey generalised this connection with friezes further, now
to $d$-angulations of the $(n+3)$-gon with $R$ basic and rigid. In this paper,
we extend these generalisations further still, to the case where the object $R$
corresponds to a general Ptolemy diagram, i.e. $R$ is basic and
$\textrm{add}(R)$ is the most general possible torsion class.
