First, a definition. Blending is the operation of taking two or more polytopes, arranging them in a compound so that some elements coincide completely, and removing those coincident pairs.

Last year, I discovered that a $4_{21}$ polytope could be vertex-inscribed in a $2_{41}$ polytope in 270 ways, and that it is possible to blend all 270 of them, giving a polytope with less than 2160*270 7-orthoplex facets. Later on, I learned that the $4_{21}$ could in fact be vertex-inscribed in *any* uniform polytope with $E_8$ symmetry. Therefore my question is: which other $E_8$-symmetric polytopes lead to blending when $4_{21}$s are vertex-inscribed in them?