Category:Face-Centered Cubic Lattices

This category contains results about Face-Centered Cubic Lattices.
Definitions specific to this category can be found in Definitions/Face-Centered Cubic Lattices.

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.