= Lattice cube
A lattice cube is a <cube> whose vertices belong to a specified <lattice>. Its three edge vectors are mutually perpendicular <lattice vectors> of equal length. In the <simple cubic lattice> $a\mathbb Z^3$, an axis-aligned cube of side $a$ is a primitive <unit cell>.
Larger cubes can have lattice vertices while enclosing many primitive cells, so “lattice cube” is a geometric condition rather than a synonym for primitive cell. For a cube of side $Na$ in that example, its volume is $N^3$ times the primitive-cell volume. Consistent shared-boundary counting assigns one lattice point to the side-$a$ cell, even though eight corner points are visible in a closed drawing.
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