
 Topological Small Triambic Icosahedron 
This is a stylized version of the small triambic icosahedron, dual of the
small ditrigonal icosidodecahedron and a stellation of the icosahedron with irregular hexagonal faces.
The idea is that only true edges of the polyhedron should connect. The
false edges that normally appear in a model where faces intersect but
don't share a true edge have been removed by cutting away part of each face,
allowing the faces to pass through each other without collision. I call this a
topological model, as it highlights the true
topology of the polyhedron. This lets you
better see the internal structure of the polyhedron.

This is how the small triambic icosahedron normally looks, before we
cut parts away.


Here's the model in Great Stella. It takes some practice to make such
a model in Stella, but it is possible! See the other topological
models for some details about how. To make this model though, you
don't need to create it yourself. You can find it in Great Stella and
Stella4D's libraries as "Stella Library→Topological→Topo
Small Triambic Icosahedron". In Stella the surface has a thickness,
but when printing the nets I only printed and used the big outer panels.


Here are the first three pieces glued together around a vertex. I used
thicker paper for this model, to add strength since it would be more
flimsy than usual. I cut the parts out completely, with no tabs, and
used thinner paper to create small caps to fit under each vertex to
hold parts together.


Same as above, but turned over and with an extra piece sitting in place
below the vertex (not glued yet).


Some more pieces. Be careful to seave the parts together properly, and
not to glue closed an area that needs another part below it.


Coming along nicely.

