The Pasch graph is the Levi graph of the Pasch configuration.
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.
Pasch Graph
See also
Pasch's Axiom, Pasch Configuration, Pasch's TheoremExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Pasch Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PaschGraph.html