

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 selfdual. 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.
 
