Other Properties
The Desargues graph has rectilinear crossing number 6, and is the smallest cubic graph with that crossing number (sequence A110507 in OEIS). It is the only known nonplanar cubic partial cube.
The Desargues graph has chromatic number 2, chromatic index 3, radius 5, diameter 5 and girth 6. It is also a 3-vertex-connected and a 3-edge-connected Hamiltonian graph.
All the cubic distance-regular graphs are known. The Desargues graph is one of the 13 such graphs.
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