The complex Witting polytope has 2160 triangular edges. The centres of these edges are shown in the next picture:
Its vertices can be subdivided in two sets of 120 vertices of 600-cells, two sets of 600 vertices of 120-cells and a set of 720 vertices of a rectified 600-cell (its vertices are the midpoints of the 720 edges of the 600-cell).
As an example I show the 8 edges that are also the edges of a complex polygon 3{3}3. I have added the four-qubit operators corresponding to the 8 vertices of the 3{3}3 and the 8 centres of its edges. The symmetry of the symbol 3{3}3 indicates self-duality. The 8 centres thus also form a 3{3}3.
The 8 four-qubit operators of the black 3{3}3 also occur in an identical shaped 3{3}3 with its 8 vertices as centres of 8 polygons 3{3}3 of the Witting polytope. I will continue in the next page with these 2160 centres.
Frans Marcelis 