Systematics and description of polyions of both linked cation- and anion-centered polyhedra with face-, edge-, and corner-sharing are discussed. Some additions to the system introduced by Liebau (1985) for cation-centered polyions are proposed which take into account the property of linking. The concept of linkedness of the polyion, ML, and the scheme of its determination are offered. A new rule of selection of fundamental chains for layers and frameworks is proposed which also considers the property of linking. For the description of topological properties of polyhedra in the polyion a diagram of connectedness (on the base of Schlegel diagrams) and a formula of connectedness are used. For the distinction of polyhedra in the polyion the concept of topological equivalence by Wells (1970) is used and the concept of configurational equivalence is proposed. Some examples of polyions composed of anion-centered tetrahedra and polyions composed of cation-centered tetrahedra are given.