Here we see how the $24$ area pieces of the Fano star generate a permutohedron. The grey edges of the diagonal triangle $I$ are ignored, and other edges have two green lines crossing them.
One hexagon on the outside creates the spherical polytope, which tiles three dimensional space. This hexagon contains three Fano star vertices $J_i$, which may be glued to form the $7$ vertices of another Fano object on the tetrahedron.
6 years ago