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 , an axis-aligned cube of side 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 in that example, its volume is times the primitive-cell volume. Consistent shared-boundary counting assigns one lattice point to the side- cell, even though eight corner points are visible in a closed drawing.
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