Augmenting the cubitruncated cuboctahedron
The cubitruncated cuboctahedron, vertex figure (8/3,6,8)
Left: Each octagonal face of the cubitruncated cuboctahedron can be augmented with a square cupola such that the triangles in the cupola are edge connected to the octagrams, the 8 in the vertex figure is replaced by a (4,3) The original vertex figures become (8/3,6,4,3) with new vertices of (4,4,4,3). The side faces of the cupolas are shown in blue and orange with the square cupola caps in yellow. All vertices are on the exterior of the figure.
Right: The above figure is shown with the square cupolas shown in framework style, a model with only one octagon augmented is linked here. A framework of the fully augmented model is linked here.