What's the maximum number of faces a convex polyhedron can have, given that it's polyhedron with all the same faces?

Question

I know there's a polyhedron named a disdyakis triacontahedron, it has 120 faces and they're all the same. Could there be a polyhedron with a larger number of faces? Can it be arbitrarily large?

Answer 1

For the non-rotational isohedra, 120 is the upper limit. But as I answered here and showed in Some Polyhedra with Identical Triangular Faces, it's possible to combine antiprisms and pyramids.

Answer 2

The wikipedia article for the disdyakis triacontahedron mentions that it is has the largest number of sides for any strictly convex polyhedron where all sides are congruent -- except for bipyramids and trapezohedra, which are two infinite families of polyhedra with this property. I think they must mean that the polyhedra need to be face-transitive, because, otherwise there's also the sandwich antiprism-bipyramid family shown by Ed Pegg.