The term "tetrahedral Johnson graph" is used in this work for a Johnson graph of the form 
(with 
), also known as an 
-tetrahedral graph (Bose and Laskar 1967). This distinguishes
these graphs from the tetrahedral
graph 
.
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.
."