Augmenting the great dodekified icosidodecahedron
The great dodekified icosidodecahedron, vertex figure (10/3,5,10/3,3)
Left: Each pentagrammic face of the great dodekified icosidodecahedron can be augmented with a pentagonal pyramid. The 5 in the vertex figure is replaced by (3,3) The original vertex figures become (10/3,3,3,10/3,3) with new vertices of (3,3,3,3,3). The triangular faces of the pyramids are shown in yellow, the original triangular faces are in blue. All vertices lie on the convex hull.
Right: The above figure is shown with the pentagonal pyramids shown in framework style. A framework of this model is linked here.