English: 5-Cube projection from the 240 vertices of the split real even E₈ Lie Group.

The basis vectors for the E₈ projection are shown (1:1 with the ring of gray vertices with the last 3 of 8 dimensions 0). There are 2480 overlapping edge lines from the 240 E₈ vertices. They have norm’d unit length calculated from the 5 non-zero projected dimensions of E₈. Of these, 32 inner vertices and 80 edges belong to the 5D 5-Cube (Penteract) proper. Edges are shown with colors assigned based on origin vertex distance from the outer perimeter. The vertex colors of the 5-Cube projection represent E₈ vertex overlaps. These are:

InView vertices=(color{overlap,count},…)Total
(LightGreen{1,20},Pink{5,20},Gray{10,10},Orange{20,1})51

All vertices=(color{overlap,count},…)Total

(LightGreen{1,20},Pink{5,100},Gray{10,100},Orange{20,20})240