  In S. Giombi, I. Klebanov, F. Popov, S. Prakash and G. Tarnopolsky, {\it
Phys. Rev.} {\bf D} 98 (2018) 10, 105005, a prismatic tensor model was
introduced. We study here the diagrammatics and the double scaling limit of
this model, using the intermediate field method. We explicitly exhibit the
next-to-leading order Feynman graphs in the $1/N$ expansion. Using appropriate
combinatorial tools, we further study the general term of the $1/N$ expansion
and we compute the $2-$point function in the double scaling limit.
