Augmenting the great icosified icosidodecahedron
The great icosified icosidodecahedron, vertex figure (6,3/2,6,5)
Each triangular face of the great icosified icosidodecahedron can be excavated with a truncated tetrahedron - vertex figure (6,6,3) - completing a cycle around the axis. This has the effect of uncrossing the original vertex figure. The 3/2 in the vertex figure is replaced by (6,6) The original vertex figure becomes (6,6,6,6,5)/2 with new vertices of (6,6,3). The original hexagonal faces of the great icosified icosidodecahedron are shown in red with the hexagonal and triangular faces of the truncated tetrahedron cyan and blue respectively. All vertices are on the exterior of the polyhedron.