**Augmenting the dodecadodecahedron**

The dodecadodecahedron, vertex figure (5,^{5}/_{2},5,^{5}/_{2})

Left: Each
pentagonal face of the dodecadodecahedron can be augmented with a pentagonal
pyramid. The 5's in the vertex figure
are each replaced by (3,3) The original vertex figures become (__3,3__,^{5}/_{2},__3,3__,^{5}/_{2})
with new vertices of (3,3,3,3,3).
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.