A polyoxyanion is a polymeric oxyanion in which multiple oxyanion monomers, usually regarded as  polyhedra, are joined by sharing corners or edges. When two corners of a polyhedron are shared the resulting structure may be a chain or a ring. Short chains occur, for example, in polyphosphates. Inosilicates, such as pyroxenes, have a long chain of  tetrahedra each sharing two corners. The same structure occurs in so-called meta-vanadates, such as ammonium metavanadate, .
The formula of the oxyanion  is obtained as follows: each nominal silicon ion () is attached to two nominal oxide ions () and has a half share in two others. Thus the stoichiometry and charge are given by:
A ring can be viewed as a chain in which the two ends have been joined. Cyclic triphosphate,  is an example.
When three corners are shared the structure extends into two dimensions. In amphiboles, (of which  asbestos is an example) two chains are linked together by sharing of a third corner on alternate places along the chain. This results in an ideal formula  and a linear chain structure which explains the fibrous nature of these minerals. Sharing of all three corners can result in a sheet structure, as in mica, , in which each silicon has one oxygen to itself and a half-share in three others. Crystalline mica can be cleaved into very thin sheets.
The sharing of all four corners of the tetrahedra results in a 3-dimensional structure, such as in quartz. Aluminosilicates are minerals in which some silicon is replaced by aluminium. However, the oxidation state of aluminium is one less than that of silicon, so the replacement must be accompanied by the addition of another cation. The number of possible combinations of such a structure is very large, which is, in part, the reason why there are so many aluminosilicates.
Octahedral  units are common in oxyanions of the larger transition metals. Some compounds, such as salts of the chain-polymeric ion,  even contain both tetrahedral and octahedral units. Edge-sharing is common in ions containing octahedral building blocks and the octahedra are usually distorted to reduce the strain at the bridging oxygen atoms. This results in 3-dimensional structures called polyoxometalates. Typical examples occur in the Keggin structure of the phosphomolybdate ion. Edge sharing is an effective means of reducing electrical charge density, as can be seen with the hypothetical condensation reaction involving two octahedra:
Here, the average charge on each M atom is reduced by 2. The efficacy of edge-sharing is demonstrated by the following reaction, which occurs when an alkaline aqueous solution of molybdate is acidified.
The tetrahedral molybdate ion is converted into a cluster of 7 edge-linked octahedra giving an average charge on each molybdenum of . The heptamolybdate cluster is so stable that clusters with between 2 and 6 molybdate units have not been detected even though they must be formed as intermediates.