**Augmenting the great vertisnub icosidodecahedron**

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

Left: Each
retrograde pentagrammic face of the great vertisnub icosidodecahedron can be
excavated with a pentagrammic
antiprism
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
(3,3,3) The original vertex figure becomes (__3,3,3__,3,3,3,3)/2
or (3^{7})/2 with new vertices of (^{5}/_{2},3,3,3).
The triangular faces of the pentagrammic antiprisms are shown in yellow. The
original triangular faces are blue. All
vertices lie on the convex hull.

Right:
Another augmentation of the great vertisnub
icosidodecahedron can be
obtained by excavating each pentagrammic face with a great
icosidodecahedron, vertex figure (^{5}/_{2},3,^{5}/_{2},3)
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) The original vertex figure becomes (4,__3, ^{5}/_{2},3__,4,3)/2
with new vertices of (

Left:
In the same way that an icosidodecahedron is
composed of two pentagonal rotundas, a great
icosidodecahedron can be thought of as being composed of two 'great'
pentagonal rotundas. A variation on the theme of the centre polyhedron
is to excavate each pentagrammic face
with such a 'great pentagonal rotunda'.
- 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) The original vertex figure becomes (4,__3, ^{5}/_{2},3__,4,3)/2
with new vertices of (

Right: A second
order augmentation can be generated from the left hand polyhedron. The
decagrammic faces of the 'great'
pentagonal rotundas can be further augmented with decagrammic
pyramids. The original vertex figures of (4,3,^{5}/_{2},3,4,3)/2
and (^{5}/_{2},3,^{5}/_{2},3) are
unchanged. The (^{5}/_{2},^{10}/_{3},3)
vertices become (^{5}/_{2},__3,3__,3), and new vertices are
added of the form (3,3,3,3,3,3,3,3,3,3)/3 - or (3^{10})/3. The
decagrammic pyramids are shown in red. All
vertices are on the exterior of the figure.