The cubic Archimedean graph on 48 nodes and 72 edges that is the skeleton of the great rhombicuboctahedron. It is implemented in the Wolfram Language as GraphData["GreatRhombicuboctahedralGraph"].
It has chromatic number 2, vertex connectivity 3, edge connectivity 3, graph diameter 9, graph radius 9, and girth 4. It is cubic, planar, and Hamiltonian. It is also zero-symmetric
It is Hamiltonian with 
Hamiltonian cycles. It has 37 distinct LCF
notations, one of order 4 (![[-11,11,-3,7,5,-9,-11,11,9,-5,-7,3]^4](/images/equations/GreatRhombicuboctahedralGraph/Inline2.svg)
), one of order 3 (
,
15, 
,
,
,
9, 7, 
,
,
15, 13, 9, 7, 
, -9, ![3]^3](/images/equations/GreatRhombicuboctahedralGraph/Inline10.svg)
), eight of order 2, and 27 of order 1. The first of these
are illustrated above.
It has graph spectrum
 |
where 
,
,
and 
are roots of 
and 
, 
, and 
are roots of 
.
It is the Cayley graph of the permutations 
1, 2, 3, 4, 5, 7, 6
, 
1, 2, 3, 4, 6, 5, 7
, 
1, 3, 2, 5, 4, 7, 6
.
