The Gosset graph is a regular graph of vertex degree 27 on 56 vertices which is the skeleton
of the Gosset polytope 
.
The Gosset graph is implemented in the Wolfram Language as GraphData["GossetGraph"].
It is a distance-regular graph with intersection array 
, and therefore also a Taylor
graph. It is also distance-transitive.
It is an integral graph with graph spectrum 
.
The graph distance graph of the Gosset graph for distance 2 is itself a distance-transitive
and distance-regular graph with intersection
array 
(and therefore another Taylor graph).
