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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