sublatture

A sublatture is a subset of points within a larger lattice that also forms a lattice. A lattice is a regular, repeating arrangement of points in space, such as the crystalline structure of a solid. For a subset of points to be considered a sublatture, two conditions must be met. Firstly, the subset must contain the origin, which is a fundamental point in any lattice. Secondly, any vector connecting two points within the subset must also connect two points within the subset. Alternatively, a sublatture can be defined as the set of points in a lattice that can be expressed as integer linear combinations of a smaller set of basis vectors. These basis vectors must themselves be vectors in the original lattice, but they span a smaller volume. The concept of sublattures is important in various fields including crystallography, solid-state physics, and the study of mathematical structures. For instance, in crystallography, the arrangement of atoms within a crystal can sometimes be described as a sublatture of a larger, more abstract lattice. Understanding sublattures helps in analyzing the symmetries and properties of complex periodic structures. They represent a more localized or reduced form of the overall periodicity present in the parent lattice.