  We illustrate how QCD color structure elegantly can be decomposed into
orthogonal multiplet bases corresponding to irreducible representations of
SU(Nc) with the aid of Wigner 3j and 6j coefficients. We also show how to
calculate the relevant 3j and 6j coefficients using multiplet bases and
birdtrack techniques and argue that only a relatively small number of Wigner 3j
and 6j coefficients are required. For up to six gluons plus quark-antiquark
pairs we explicitly calculate all 6j coefficients required for up to NLO
calculations.
