  We use the relation of the one-loop subleading-color amplitudes to the
one-loop $n$-point leading color amplitudes in ${\cal N}=4$ SYM, to derive a
polytope interpretation for the former in the $MHV$ case, and a representation
in momentum twistor space for the general $N^kMHV$ case. These techniques are
explored in detail for the 5-point and 6-point amplitudes. We briefly discuss
the implications for IR divergences.
