Rotation of the E8 root system

(See the description of for more about E_8 and its root system.) The root system of E_8, an 8-dimensional polytope also known as the Gosset 4_21 polytope (here projected on a 2-plane that initially shows a 24-fold symmetry), is made to rotate uniformly, at a constant rate (technically: along a one-parameter subgroup). The polytope shown is always the same, it is merely rotated in 8-dimensional space, always in the same manner. The rotation chosen here is special