Definition:Face-Centered Cubic Lattice

Definition

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

$\tuple {\dfrac 1 2 a x, \dfrac 1 2 a y, \dfrac 1 2 a z}$

such that:

$a$ is a positive real constant

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

$x + y + z$ is an even integer.

Also known as

A face-centered cubic lattice can also be presented as face-centred cubic lattice, using the British English centre rather than center.

Also see

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

• Results about face-centered cubic lattices can be found here.

Sources

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