The Games graph is a strongly regular graph on 729 vertices with parameters 
.
It is distance-regular but not distance-transitive with intersection
array 
and has graph spectrum 
.
It is implemented in the Wolfram Language as GraphData["GamesGraph"].
It can be constructed as follows. There is a unique 56-cap in 
(i.e., the set of 56 points such that any line meets
it in at most two points) (Hill 1978). Taking the as vertices the points of 
and joining two vertices when
the line through the points meets the hyperplane at infinity in a point of the cap
gives the Games graph (Cameron 1975, Games pers. comm. to Brouwer and van Lint 1984).
." J. Combin. Th. (B) 103, 521-531,
2013.Brouwer, A. E. and van Lint, J. H. "Strongly Regular
Graphs and Partial Geometries." In