The cuboctahedral graph is an Archimedean quartic symmetric graph on 12 nodes and 24 edges that is the skeleton of the cuboctahedron, as well as the uniform cubohemioctahedron and octahemioctahedron.
It is planar, has graph diameter 3, graph radius 3, and is Hamiltonian.
It is implemented in the Wolfram Language as GraphData["CuboctahedralGraph"].
The cuboctahedral graph is the line graph of the cubical graph.
It has chromatic number 3, and chromatic polynomial
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The cuboctahedral graph is an integral graph with graph spectrum 
. Its automorphism
group has order 
.
The bipartite double graph of the cuboctahedral graph is the rolling polyhedron graph of the cube.
