  Inspired by the recent work of Nima Arkani Hamed and collaborators who
introduced the notion of positive geometry to account for the structure of
tree-level scattering amplitudes in bi-adjoint $\phi^3$ theory, which led to
one-loop descriptions of the integrands. Here we consider the one-loop
integrals themselves in $\phi^3$ theory. In order to achieve this end, the
geometrical construction offered by Schnetz for Feynman diagrams is hereby
extended, and the results are presented. The extension relies on masking the
loop momentum variable with a constant and proceeding with the calculations.
The results appear as a construction given in a diagrammatic manner. The
significance of the resulting triangular diagrams is that they have a common
side amongst themselves for the corresponding Feynman diagrams they pertain to.
Further extensions to this mathematical construction can lead to additional
insights into higher loops. A mathematica code has been provided in order to
generate the final results given the initial parameters of the theory.
