A n-dipyramidal graph is the skeleton of an n-sided dipyramid. It has vertex count n+2 and edge count 3n. The 3-dipyramidal graph is the unique graph K_5-e obtained by removing any single edge from the pentatope graph K_5. Special cases are summarized in the following table. n graph 3 12-Johnson skeleton graph 4 octahedral graph 5 32-Johnson skeleton graph