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.

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