  We present compact analytic formulae for the one-loop amplitudes for Higgs +
4 parton scattering, $0 \to g g g g h$, $0 \to \bar{q} q gg h$ and $0\to
\bar{q} q \bar{q}^\prime q^\prime h$, mediated by a loop of massive coloured
quarks. We exploit the correspondence with a theory in which a massive coloured
scalar circulates in the loop to avoid a proliferation in the number of terms
in the result. In addition, we use momentum twistors and high precision
numerical evaluations to simplify the expressions. The analytic results in this
paper, in terms of spinor products, allow construction of an efficient
numerical program to calculate the amplitude.
