By introducing four potential functions, the governing equations of plane problems inicosahedral quasicrystal media are composed of four second-order partial differential equations, inwhich the displacement components are the essential unknowns. The general solution of theseequations is further established, and all expressions for the phonon and phason fields are expressedin terms of the potential functions. As an application of the general solution, the closed formsolutions are obtained for wedge problems subjected to point phonon force and phason force at theapex.