The term "Goedgebeur configuration" is a name proposed here for the self-dual configuration whose Levi graph is the Goedgebeur
graph. It admits a geometric realization by points and lines due to Gábor
Gévay (M. Abreu, pers. comm., May 12, 2026), a particular realization
of which is illustrated above (E. Weisstein, May 22, 2026).
The graph corresponding to the Goedgebeur configuration will be implemented in a future version of the Wolfram Language as GraphData["GoedgebeurConfigurationGraph"].