File:Weak orderings 4 Hasse.svg

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Cayley graph

Cayley graph related to the permutohedron of order 4 with k-faces labelled with weak orderings

Geometrically this is the face lattice of the truncated octahedron (without the empty face).
It has Sloane's A000670(4) = 75 nodes and 158 edges.

This is like a Hasse diagram with the outer nodes finer than those on the inside.


Reading the permutation matrices by row gives the permutations in the Cayley graph, which also appear as labels a|b|c|d.
(Reading them by column gives the permutations in the permutohedron.)

There is also:
left action
last ⋅ first
This is:
right action
first ⋅ last


This SVG was created with Inkscape, and uploaded with Commonist.
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Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
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