Linear density of atoms can be defined as number of atoms centered on a direction vector / length of direction vector. Similarly planar density of atoms is number of atoms centered on a plane / area of plane. Linear density and planar density are important considerations during deformation and "slip"; planes tend to slip or slide along planes with high planar density along directions with high linear density. Based on these values {111} planes have the following unique characteristics:

The crystal growth is easiest

The chemical etching is slowest

Tensile strength is highest

Modulus of elasticity is highest

It is the typical cleavage plane