Antipodal self-duality of square fishnet graphs

In strongly-deformed planar ${\cal N}=4$ super-Yang-Mills theory, or fishnet theory, a point-split single-trace correlation function of four dimension-$m$ scalar operators is given by a single Feynman integral, which involves integrating over locations of a $m\times m$ grid of points. We show that for any integer $m$ this square fishnet graph is invariant under the combined action of a kinematic map and the antipode map of the Hopf algebra on multiple polylogarithms, i.e. it possesses an antipodal self-duality.