Johnson's solids are covered only regular polygons.

They say V.A.Zalgaller concluded that Johnson's solids contain 92 kinds of polyhedra.

But, I could put the following twin polyhedra by 12 pentagons and 24 triangles of POLYDRON with few distortion.

V 20(3,3,5,5)

V 8(3,5,3,5)

V 4(3,3,3,3,5)