  Shimura curves are moduli spaces of abelian surfaces with quaternion
multiplication. Models of Shimura curves are very important in number theory.
Klein's icosahedral invariants $\mathfrak{A},\mathfrak{B}$ and $\mathfrak{C}$
give the Hilbert modular forms for $\sqrt{5}$ via the period mapping for a
family of $K3$ surfaces. Using the period mappings for several families of $K3$
surfaces, we obtain explicit models of Shimura curves with small discriminant
in the weighted projective space ${\rm Proj}
(\mathbb{C}[\mathfrak{A},\mathfrak{B},\mathfrak{C}])$.
