A unit hypercube of n dimensions is the convex hull of the points given by all sign permutations of the Cartesian coordinates \left(\pm \frac{1}{2}, \pm \frac{1}{2}, \cdots, \pm \frac{1}{2}\right).
An n-dimensional hypercube is also often regarded as the convex hull of all sign permutations of the coordinates (\pm 1, \pm 1, \cdots, \pm 1).