Let's use this fact to find a unit cell by enumerating all such translations. Symmetries map vertices to vertices, so the first vertex (lexicographically sorted by position) is mapped to another. But since the first vertex was put in position 0 3 , the translation is directly given by the position of the other vertex. Hence, only n -1 translations need to be checked, and if none is valid then the initial cell is a unit cell.