Solution: A regular octahedron has six vertices, with pairs at $ (\pm1, 0, 0) $, $ (0, \pm1, 0) $, and $ (0, 0, \pm1) $. Given three vertices, the missing vertex must be $ (0, 0, 1) $ or $ (0, 0, -1) $. Since the problem specifies integer coordinates, both are valid, but the fourth vertex (completing the octahedron) is $ (0, 0, 1) $. - Veritas Home Health