Firstly, a definition:
A convex polyhedron, whose faces are regular polygons (2D polytopes).
This includes the 92 Johnson solids, 13 Archimedean solids, 5 Platonic solids and two infinite familes - prisms and antiprisms.
However, I see two ways of extending this definition to 4D:
1) A convex polychoron (4-polytope), whose 2D faces are regular polygons, ie. its 3D faces satisfy the first definiton.
2) A convex polychoron, whose 3D faces are regular polyhedra (3D polytopes).
The list I gave above is known to be complete. But is there (at least partial) progress on the 4D case? The second definition is much more restrictive, so maybe a complete classification of polychora, which satisfy 2) exists. Can you point me to some reference, please?