Augmenting the great dodecahedron
The great dodecahedron, vertex figure (5,5,5,5,5)/2
Left: Each pentagonal face of the great dodecahedron can be excavated with a pentagonal prism completing a cycle around the axis. The 5's in the vertex figure are each replaced by (4,4) The original vertex figures become (4,4,4,4,4,4,4,4,4,4)/3 or (410)/3 with new vertices of (5,4,4). All vertices lie on the convex hull.