Augmenting the small ditrigonal icosidodecahedron
The small ditrigonal icosidodecahedron, vertex figure (5/2,3,5/2,3,5/2,3)
Each pentagrammic and triangular face of the small ditrigonal icosidodecahedron can be excavated with a pentagrammic prism and a triangular prism respectively, each of which completes a cycle around the axis. The 5/2 and the 3 in the vertex figure are each replaced by (4,4) The original vertex figures become (4,4,4,4,4,4,4,4,4,4,4,4)/5 or (412)/5 with new vertices of (5/2,4,4) and (3,4,4). The square faces of the pentagrammic prisms are shown in orange with the square faces of the triangular prisms in yellow. All vertices are on the exterior of the figure.