In eight-dimensional geometry, a hexicated 8-simplex is a uniform 8-polytope, being a hexication (6th order truncation) of the regular 8-simplex.
Hexicated 8-simplexes Wikipedia
The Cartesian coordinates of the vertices of the hexicated 8-simplex can be most simply positioned in 8-space as permutations of (0,0,0,1,1,1,1,1,2). This construction is based on facets of the hexicated 9-orthoplex.
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.