General and special position

For any plane group we may locate an object (a colored circle for example) anywhere within the unit cell. In some specific positions, the object and some of its symmetry-generated equivalents may converge into a single point. This single point is called a special position. All the others are general positions.

It is easy to see that the number of symmetry-equivalent points in each unit cell depends on the point's position. The number is largest for general positions and smaller on special positions. The number of symmetry-equivalent positions on special positions is always an integral fraction of the largest possible number.

This concept of general and special positions is important and is directly linked to the stoichiometry as expressed by the chemical formula of a crystalline sample.