Exploiting the 1,440-fold symmetry of the master two-loop diagram

The 1,440-element symmetry group of the generic two-loop diagram of massless scalar field theory in 4-2ω dimensions is computed, using tetrahedral symmetry and star-triangle duality. Constructing all quadratic and quartic polynomial invariants, we expand the diagram through O(ω5), where one first encounters a coefficient that does not appear to be expressible in terms of the Riemann zeta function, thereby strengthening previous suspicions that genuinely new calculational complexity arises at the level of 6-loop renormalization. (orig.)