To the best of my recollection, the "eutactic stars" discussed by Coxeter in Regular Polytopes all yield projections from n-dimensional hypersolids (n > 3) to their "shadows" as familiar solids in 3-space.
Does anyone know of any "eutactic hyperstars" which fulfill the same role between j- and k-space, for j > k > 3 ?
I would be particularly interested in any such cases where j = 8 and k = 6, because I think they might shed light on whether there is an answer to a question which I recently posted: