An article (interview) with John Baez used an E8 projection which I introduced to Wikipedia in Feb of 2010 here. Technically, it is E8 projected to the E6 Coxeter plane.

The projection uses X Y basis vectors of:

X = {-Sqrt[3] + 1, 0, 1, 1, 0, 0, 0, 0};

Y = {0, Sqrt[3] – 1, -1, 1, 0, 0, 0, 0};

Resulting in vertex overlaps of:

24 Yellow with 1 overlap

24 Dark Blue each with 8 overlaps (192 vertices)

1 Light Blue with 24 overlaps (24 vertices)

After doing this for a few example symmetries, Tom took my idea of projecting higher dimensional objects to the 2D (and 3D) symmetries of lower dimensional subgroups – and ran with it in 2D – producing a ton of visualizations across WP. 🙂

It was one of those that was subsequently used that article from the 4_21 E8 WP page.

Here is a representation of E6 in the E6 Coxeter plane:

Resulting in vertex overlaps of:

24 Yellow with 1 overlap

24 Orange each with 2 overlaps (48 vertices)