Interestingly, these 2D and 3D projections includes all 240 vertices and 6720 edges of E8 with the same 2D and 3D projection. Only the vertex and edge overlap are different.

The D6 to H3 projection based on 3 rows of the E8 to H4+H4 Phi folding matrix.

The rotation off of the D6 to H3 projection based on the E8 to H4+H4 Phi folding matrix is

Using this rotated basis, we now show rectified D6 (Cantellated 6-Orthoplex t0,2{3,3,3,3,3,4})

Bi-rectified D6

6-Orthoplex

Rectified 6-Orthoplex (D6)

Bi-Rectified 6-Orthoplex

Tri-Rectified 6-Orthoplex