A 
-dipyramidal graph is the skeleton of an 
-sided dipyramid. It is isomorphic to the 
-cone graph 
, where 
is a cycle graph, 
is the empty graph on 2 vertices, and 
denotes a graph join.
The 
-dipyramidal graph has vertex count 
and edge count 
. Dipyramidal graphs are pancyclic.
The 3-dipyramidal graph is the unique graph 
obtained by removing any single edge from the pentatope graph 
.
Special cases are summarized in the following table.
