Definition:Cubic Lattice

Definition

A cubic lattice is a set of points in Cartesian $3$-space whose coordinates are of the form:

$\tuple {a x, a y, a z}$

such that:

$a$ is a positive real constant

$x$, $y$ and $z$ are integers.

Three-Dimensional Integer Lattice

The $3$-dimensional integer lattice is the cubic lattice where $a = 1$.

That is, it is the set of points in Cartesian $3$-space whose coordinates are of the form:

$\tuple {x, y, z}$

such that $x$, $y$ and $z$ are integers.

Also see

• Definition:Body-Centered Cubic Lattice
• Definition:Face-Centered Cubic Lattice

• Kepler's Conjecture

• Results about cubic lattices can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cubic lattice