  We present the calculation of the three distinct non-planar hexa-box
topologies for five-point one-mass processes. These three topologies are
required to obtain the two-loop virtual QCD corrections for two-jet-associated
W, Z or Higgs-boson production. Each topology is solved by obtaining a pure
basis of master integrals and efficiently constructing the associated
differential equation with numerical sampling and unitarity-cut techniques. We
present compact expressions for the alphabet of these non-planar integrals, and
discuss some properties of their symbol. Notably, we observe that the extended
Steinmann relations are in general not satisfied. Finally, we solve the
differential equations in terms of generalized power series and provide
high-precision values in different regions of phase space which can be used as
boundary conditions for subsequent evaluations.
