The McLaughlin geometry is a non-existent partial geometry 
whose point graph would be the McLaughlin
graph and whose lines would make that graph a geometric
graph. The existence of such a geometry was a long-standing open problem motivated
by the exceptional properties of the McLaughlin graph,
which has strongly regular graph parameters
.
Östergård and Soicher (2016) proved that no partial geometry with parameters 
exists. In particular, the McLaughlin
graph is a pseudogeometric graph for
but is not the point graph of a partial
geometry.
