  We compute the number of $\mathcal{X}$-variables (also called coefficients)
of a cluster algebra of finite type when the underlying semifield is the
universal semifield. For classical types, these numbers arise from a bijection
between coefficients and quadrilaterals (with a choice of diagonal) appearing
in triangulations of certain marked surfaces. We conjecture that similar
results hold for cluster algebras from arbitrary marked surfaces, and obtain
corollaries regarding the structure of finite type cluster algebras of
geometric type.
