# mg.metric geometry – When does blending occur?

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?