The Pasch graph is the Levi graph of the Pasch configuration.
The Pasch graph is implemented in the Wolfram Language as GraphData["PaschGraph"].
The Pasch graph is edge-transitive but not vertex-transitive, but fails to be semisymmetric since it is not regular. Its line graph is the truncated tetrahedral graph.
The Pasch graph is also its own distance-3 graph distance graph.
The Pasch graph is an outer-cylindrical forbidden minor 
(No. 38; Archdeacon et al. 2001).
