**Augmenting the great stellated dodecahedron**

The great stellated dodecahedron, vertex figure (^{5}/_{2},^{5}/_{2},^{5}/_{2})

Left: Each
pentagrammic face of the great stellated dodecahedron can be excavated with a pentagrammic
pyramid completing a cycle around the axis. Each ^{5}/_{2} in the vertex figure is replaced by
(3,3) The original vertex figure becomes (__3,3__,__3,3__,__3,3__)/2
with new vertices of (3,3,3,3,3)/2. All
vertices are on the exterior of the polyhedron.

Right: Each
pentagrammic face of the great stellated dodecahedron can be excavated with a pentagrammic
prism completing a cycle around the axis. Each ^{5}/_{2} in the vertex figure is replaced by
(4,4) The original vertex figure becomes (__4,4__,__4,4__,__4,4__)/2
with new vertices of (^{5}/_{2},4,4). All
vertices are on the exterior of the polyhedron. This example was
discovered by Mason Green in 2005.