[1] The Foster graph is Hamiltonian and has chromatic number 2, chromatic index 3, radius 8, diameter 8 and girth 10.

It has queue number 2 and the upper bound on the book thickness is 4.

It is the unique distance-transitive graph with intersection array {3,2,2,2,2,1,1,1;1,1,1,1,2,2,2,3}.

[4] It can be constructed as the incidence graph of the partial linear space which is the unique triple cover with no 8-gons of the generalized quadrangle GQ(2,2).

It is one of a finite number of such graphs with degree six.

[6] It acts transitively on the vertices, on the edges and on the arcs of the graph.

[7] The characteristic polynomial of the Foster graph is equal to