by **quickfur** » Thu Nov 30, 2017 5:13 pm

I think the OP wasn't looking for a uniform solution, which is (probably?) impossible.

Also, I think lace prisms are kinda cheating, because they are ultimately just derivations / elaborations of prisms.

My guess is that the OP is looking for a polyteron where 120-cell family polychora serve as facets that don't lie in parallel 4-planes. Now obviously if you relax the uniform requirement you'll always be able to find something, so there ought to be some restriction on what other facets there can be. A loose restriction is being CRF, but that would be hard to find a solution for since we don't know the full set of 4D CRFs yet. A tighter restriction is that all facets must be uniform, though the overall polyteron may not be. I'm not sure there's a solution in that case, but maybe it's possible.

An even tighter restriction is if we add the requirement that the overall polyteron must have some symmetry group higher than prismatic symmetry (or even asymmetrical, as would be in the CRF case in general). I'm not 100% sure if this is possible, but perhaps there is a way to do this? E.g., take a uniform polyteron that has 16-cell facets, substitute that with snub 24-cells, then cap them with pyramids to make 600-cells, then expand / modify the rest of the polyteron accordingly so that the remaining gaps can be closed up with uniform (or CRF?) pieces.