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. 

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