Final answer:
Cubic unit cells cannot have an end-centered variation as it would disrupt the symmetry and packing efficiency intrinsic to the cubic crystal systems, which only accommodate corner, face-centered, and body-centered lattice points.
Step-by-step explanation:
Cubic unit cells cannot have an end-centered variation because in the cubic system, the atoms or ions are symmetrically disposed only at the corners, in the body center, or in the face centers of the cube.
The cubic crystal system includes simple cubic, face-centered cubic (FCC), and body-centered cubic (BCC) structures. In the simple cubic structure, each corner atom is shared by eight unit cells, resulting in only one-eighth of each atom being within a specific unit cell.
The FCC structure includes atoms at the corners and the center of each face of the unit cell, with each corner atom shared by eight unit cells, and each face atom shared by two. The BCC has a central atom entirely contained within the unit cell, in addition to the corner atoms.
If a cubic unit cell was end-centered, it would disrupt the inherent symmetry and packing efficiency of the cubic crystal systems, as none of the cubic systems allows for end-centered lattice points due to their geometric constraints and atomic packing considerations.