The truncated octahedral graph is the cubic Archimedean graph on 24 nodes and 36 edges that is the skeleton
of the truncated octahedron. It is isomorphic
to the Bruhat graph 
, meaning it is the graph having have all permutations
of 
as vertices with an edge between pairs of permutations
that differ by an adjacent transposition.
It is implemented in the Wolfram Language as GraphData["TruncatedOctahedralGraph"].
The truncated octahedral graph is vertex-transitive but not edge-transitive. It is Hamiltonian.
It has LCF notations ![[3,-7,7,-3]^6](/images/equations/TruncatedOctahedralGraph/Inline3.svg)
, ![[5,-11,11,7,5,-5,-7,-11,11,-5,-7,7]^2](/images/equations/TruncatedOctahedralGraph/Inline4.svg)
, and [
, 5, 
, 
, 
, 3, 
, 5, 
, 9, 7, 3, 
, 11, 
, 7, 5, 
, 
, 9, 7, 
, 
, 3].
It has graph spectrum 
. Its
automorphism group is of order 
.
