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?