  Inspired by the topological sign-flip definition of the Amplituhedron, we
introduce similar, but distinct, positive geometries relevant for one-loop
scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory. The
simplest geometries are those with the maximal number of sign flips, and turn
out to be associated with chiral octagons previously studied in the context of
infrared (IR) finite, pure and dual conformal invariant local integrals. Our
result bridges two different themes of the modern amplitudes program: positive
geometry and Feynman integrals.
