In the parametric representation, Feynman integrals can be viewed as Euler integrals defined by the Symanzik polynomials of a graph. The convergence properties of these integrals are intimately tied to the combinatorial geometry of their associated Newton polytopes; specifically, finiteness is guaranteed when the polytope contains interior points. We present a classification of Feynman integrals associated with polytopes containing a unique interior point, identifying a subset that are reflexive. Our results show that such reflexive polytopes are surprisingly scarce within the space of Feynman graphs. We conclude by displaying an exact expression for the multiloop sunset integral above threshold and its mirror symmetric interpretation.
This is based on a joint work with Leonardo de la Cruz and Pavel Novichkov [arXiv:2512.10518] and on [arXiv:2603.03183]