simple, diameter
Q4 is the only (combinatorial type of) simple 9-facet 4-polytope with diameter 5.
174, 166, 165
27
9
1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1