This is a shot of the relevant Mathematica code snippets that produce the images:

E8 4_21 (with projection basis, edges, vertex overlap colors & counts) (click here for very large SVG):

E8 2_41 (with projection basis, vertex overlap colors & counts) (click here for very large SVG):

E8 1_42 (with projection basis,vertex overlap colors & counts) (click here for very large SVG):

Files of the actual vertex lists:

E8-4_21.txt (240)

E8-2_41.txt (2160) (EVEN +/- signs on some vertices producing incorrect projections)

E8-1_42.txt (17280) (EVEN +/- signs on some vertices producing incorrect projections)