The three-dimensional lattice may be thought of as created of various sets of parallel planes. Each set of planes has a particular orientation in space. The space position of any crystallographic plane is determined by three lattice points not lying on the same straight line.

What is dimension of a lattice?

The integers n and k are called the dimension and rank of the lattice. If n = k then L(B) is called a full rank lattice. 1Technically, closure under subtraction is enough because addition can be expressed as a + b = a − (−b).

What is meant by 3 dimensional lattice arrangement within a mineral?

A crystalline solid is a three-dimensional structure in which the constituents (i.e., atoms, ions, or molecules) are arranged in a definite repeating pattern. The positions of the constituents' centers are represented by points on a three-dimensional lattice.