Augmenting the small cubicuboctahedron
The small cubicuboctahedron, vertex figure (4,8,3/2,8)
Each triangular face of the small cubicuboctahedron can be excavated with a snub cuboctahedron, vertex figure (4,3,3,3,3) completing a cycle around the axis. The octahedral triangular face is used for the excavation. This has the effect of uncrossing the original vertex figure. The 3/2 in the vertex figure is replaced by (3,4,3,3) The original vertex figure becomes (4,8,3,4,3,3,8)/2 with new vertices of (4,3,3,3,3). Triangular and square faces of the snub cuboctahedron are shown in blue and yellow respectively. All vertices are on the exterior of the polyhedron.
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