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).

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and S. A. Vanstone). Toronto, Canada: Academic Press, pp. 85-122,
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§10.75 in Strongly
Regular Graphs. Cambridge, England: Cambridge University Press, p. 354-355,
2022.Cameron, P. J. "Partial Quadrangles." Quart.
J. Math. Oxford26, 61-73, 1975.DistanceRegular.org. "Games
graph." https://www.distanceregular.org/graphs/games.html.Games,
R. A. "The Packing Problem for Finite Projective Geomeries." Ph.D.
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