The exceptional symmetry of E8

Here's a little movie I made about the Lie group E₈:

Out of all the known Lie groups, E₈ stands out as the largest and most complex exceptional group. It has 248 generating elements, which by themselves have an astounding degree of symmetry. This symmetry can only be fully grasped in 8-dimensional space. But luckily it is also possible to project E₈ onto a two-dimensional plane, chosen such that the resulting image preserves a small fraction of its total symmetry. There are different choices for these two-dimensional planes, some preserving more symmetry than others. The movie rotates through a selection of these planes in succession.