with a consideration of $S_4$, the permutations on four letters. Recall that this group describes a 24 vertex permutohedron polytope in three dimensions, which is a hexagonal version of the Stasheff polytope for the pentagon. Ma thinks in terms of a SUSY seesaw model for mass matrices. On reduction of the parameters, his neutrino matrix now becomes a degenerate 1-circulant
with $a$ on the diagonal.
We associated $3 \times 3$ 1-circulants with vertices of a hexagon, which comes from the cube. A cube has the symmetry group $S_4$, but in operad land it is more natural to relate the cube to the permutohedron via the Loday-Ronco