The above sketch indicates one way to apply the elements of S4
to the Aitchison cuboctahedron . It is a rough sketch illustrating a
correspondence between four edge-hexagons and four label-sets.
The labeling is not as neat as that of a permutahedron by S4
shown below, but can perhaps be improved.
Permutahedron labeled by S4 .
Update of 9 PM EDT June 1, 2019 —
. . . And then of course there is the obvious labeling derived from
the above permutahedron —
