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.