**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.