  For a field $F$ and a given integer $n>1$, Goncharov has given a complex
$\Gamma_F(n)$ which he calls motivic and which he expects to rationally compute
the weight $n$ motivic cohomology of $\text{Spec }F$, and hence its algebraic
$K$-groups in Adams weight $n$, and he was also led to---conjecturally
quasiisomorphic---`thickened' complexes thereof. These complexes involve tensor
products of higher Bloch groups, the latter having been linked to the geometry
of certain configurations in Goncharov's proof of Zagier's Polylogarithm
Conjecture for weight 3, and an analogous picture has long been envisioned by
Goncharov for higher weight as well.
  We provide a partial morphism in weight 4 by giving three out of four maps
for configurations in general position.
