  The method of using Hopf algebras for calculating Feynman integrals developed
by Abreu et al. is applied to the two-loop non-planar on-shell diagram with
massless propagators and three external mass scales. We show that the existence
of the method of cut Feynman diagrams comprising of the coproduct, the first
entry condition and integrability condition that was found to be true for the
planar case also holds for the non-planar case; furthermore, the non-planar
symbol alphabet is the same as for the planar case.n These are the main results
of this work, and they have been obtained by a systematic analysis of the
relevant cuts, using the symbolic manipulation codes HypExp and PolyLogTools.
The obtained result for the symbol is cross-checked by an analysis of the known
two-loop original Feynman integral result.
