A Johnson graph of the from 
(with 
) is known as an 
-tetrahedral graph. To avoid confusion with the tetrahedral
graph 
,
such graphs are known in this work as tetrahedral Jonson graphs. The tetrahedral
Johnson graphs are distance-regular and
geometric.
The 6-tetrahedral Johnson graph is a distance-regular graph with intersection array 
, and therefore also a Taylor
graph.
