I am repeatedly amazed by the number
of polyhedra that have 'great' isomorphs. I have yet to see a formal
definition 'great' when applied to polyhedra, but my understanding of it is that
certain polygons such as {5}, {8}, or {10}-gons
can be replaced by {^{5}/_{2}}, {^{8}/_{3}} or {^{10}/_{3}}-gons
respectively, vertices are crossed and
the symmetry of the original figure retained. I am aware though that this prefix is normally reserved for Uniform
Polyhedra.

In investigating the Stewart Toroid
**T5 / 12 Q5S5 (D5) **(above
left) , I was delighted to
discover that even Stewart Toroids can have 'great' isomorphs. In the same
way that a truncated dodecahedron can be tunnelled by twelve pentagonal cupolas
and twelve pentagonal antiprisms, with a central dodecahedron then removed, then
a great stellated truncated dodecahedron (with vertex figure ^{10}/_{3},^{10}/_{3},3)
can be 'drilled' by twelve {5/3}-cupolas, and twelve {5/3}-antiprisms (these are
retracted) with the final removal of a central core of a great stellated
dodecahedron. Like the original figure, it is also genus 11. In pseudo-Stewart
terminology, you have a **tE* / 12 Q{5/3}S{5/3} (E*)**
(above right).
This is isomorphous to the original Stewart Toroid.

Again like the original figure it contains the**
L1-L1'** and **L2-L2'** layers. A fascinating figure can be obtained
by taking the slice between the L2-L2' layers and filling the holes with
pentagrams (above right). As a toroid it seems
slightly disappointing but I like the 'fractal-like' appearance of the
overlapping pentagrammic faces.