**Augmenting the vertisnub dodecadodecahedron**

The vertisnub dodecadodecahedron, vertex figure (^{5}/_{3},3,5,3,3)

Left: Each pentagrammic face of the vertisnub
dodecadodecahedron can be
excavated with a small ditrigonal icosidodecahedron,
vertex figure (3,^{5}/_{2},3,^{5}/_{2},3,^{5}/_{2})
completing a cycle around the axis. This has the effect of uncrossing the original
vertex figure. The ^{5}/_{3} in the vertex figure is replaced by
(3,^{5}/_{2},3,^{5}/_{2},3) The original vertex figure becomes
__ (3, ^{5}/_{2},3,^{5}/_{2},3__,3,5,3,3) with new vertices of
(3,

Right: Dr
Richard Klitzing has explored the facetings
of the small ditrigonal icosidodecahedron. One faceting, which he
terms 'sid-6-10-0-2' has the necessary 5-fold pyramidical symmetry around a pentagrammic face
and is also locally convex. As the vertices of the sid-6-10-0-2 are a
subset of the vertices of the small ditrigonal icosidodecahedron
then excavating each pentagrammic face of the vertisnub
dodecadodecahedron with the sid-6-10-0-2 will also
generate a valid augmented polyhedron. The ^{5}/_{3} in the vertex figure is
again replaced by
(3,^{5}/_{2},3,^{5}/_{2},3). The original vertex figure
again becomes
__ (3, ^{5}/_{2},3,^{5}/_{2},3__,3,5,3,3).
New vertices are now though of the form (