As with the associahedron, we may pull some faces of the permutohedron up onto three faces of a tetrahedron.

This puts the $7$ points of a Fano plane inside $7$ out of the $8$ hexagonal faces. Note how the upper triangles form a shadow Fano plane for the Fano plane on the base triangle.

6 years ago

So we are seeing the natural creation truncated tetrahedra, whereby one vertex of (say) an associahedron becomes three vertices.

ReplyDeleteYou know, it really is time those twistor people started learning some category theory.

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