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.