The Foster graph is one of the 13 such graphs. 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}.
The Foster graph belongs to a group of 13 such graphs. It is distinguished by being the only distance-transitive graph characterized by its unique vertex degree sequence: {3,2,2,2,2,1,1,1;1,1,1,1,2,2,2,3}.