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Noble Faceting of Snub Cube

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A faceting of the snub cube, meaning they share the same vertices. Discovered by yours truly, Robert Webb, in 2008, this polyhedron is special because it is noble, meaning all faces are symmetrically identical (isohedral), and all vertices are also symmetrically identical (isogonal). Max Brückner studied such polyhedra (and compounds) in 1906, and it appears this may be the first addition to the set since then (over 100 years ago!), aside from some degenerate cases where faces visit the same vertex more than once while traversing their edges.

The polyhedron also has the unusual property of being self-dual.

I discovered this noble polyhedron using new features of Great Stella/Stella4D. These were not made public at the time, but are now available as of version 5.0. Stella can now find facetings for you, allowing you to step through them one by one by hitting the Up Arrow key in the Faceting Preview window. The new "Faceting" menu includes the "Faceting→Maximum Facet Types" option. Set this to "1" to ensure you only find isohedral polyhedra and compounds. Now hitting the Up Arrow with the snub cube loaded takes you straight to this new noble polyhedron!

My model of this polyhedron uses 4 colors, the minimum required to ensure that no faces of the same color intersect or share an edge.

I first announced this new polyhedron on my forums here. You'll also find a photo of Ulrich Mikloweit's amazing model of it in that thread.

The faces are irregular pentagons. This screenshot shows which facet of the snub cube to create in order to generate the model.
There are 3 different pieces involved, and you'll need 24 of each. My model has 4 different colors, so 6 copys of each part are required in each of the 4 colors.
Start fitting the pieces together like this. Be careful with the coloring.
At this stage the model seemed a bit flexible, so I put some extra support inside. I used two kinds. One was simply a straight piece of card across the tabs inside the point where edges intersect each other under the 4-fold symmetry axes. The other can be created as a facet as shown here, using Stella's Faceting Mode.
You can see the two kinds of internal support added here. This really helped to make it a solid model.
Getting near the end here, but time to think about how that last piece is going to be put in! I decided it might be best to put the last piece on as a cap.
Instead of continuing as before, I printed some larger pieces to attach as seen here.
A separate cap, seen here, can then be glued down onto the larger parts above to finish the model.
Another photo of the finished model.

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