I've recently been doing a search for these (A polychoron is a 4D polytope made up of polyhedra, like a polyhedra 3D made up of polygona)

The properties are:

1) Strictly-convex from body to cell (this is generalising it to higher dimensions)

2) Non-vertex transitive

3) Regular faced

I found 193 of these so far and hope to find more

They're based on the Johnson Solids