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I think it would be pretty useful if you can facet vertex figures, or have a faceting which retains the edges of a polytope.

Both good ideas. Might be a while before I can look into adding them, but I'll add them to the to-do list.

Thanks!

Both ideas are the same actually, since the vertices of a vertex figure correspond to edges on a polyhedron. For 4d polychora, you might also want to implement the ability to edge facet vertex figures, to have polychora which share the same faces.

Not quite the same necessarily. Faceting a vertex figure could allow you to cut across the vertex figure, eg to make the pentagram face of a small stellated dodecahedron from the pentagonal vertex figure of an icosahedron.

I imagine clicking on a vertex in the vertex figure would add a vertex to the new facet. I'm not sure it's any more useful than just doing it in the 3D view though. Not sure how you're picturing it working.

Intersecting idea about faceting 3D vertex figures for 4D polytopes.