  We construct algebraic cycles in Bloch's cubical cycle group which correspond
to multiple polylogarithms with generic arguments. Moreover, we construct out
of them a Hopf subalgebra in the Bloch-Kriz cycle Hopf algebra. In the process,
we are led to other Hopf algebras built from trees and polygons, which are
mapped to the latter. We relate the coproducts to the one for Goncharov's
motivic multiple polylogarithms and to the Connes-Kreimer coproduct on plane
trees and produce the associated Hodge realization for polygons.
