  We clarify the relationship between different multiple polylogarithms in
weight~4 by writing suitable linear combinations of a given type of iterated
integral I_{n_1,...,n_d}(z_1,...,z_d), in depth d>1 and weight \sum_i n_i=4 in
terms of the classical tetralogarithm Li_4. In the process, we prove a
statement conjectured by Goncharov which can be rephrased as writing the sum of
iterated integrals I_{3,1}(V(x,y),z), where V(x,y) denotes a formal version of
the five term relation for the dilogarithm, in terms of Li_4-terms (we need 122
such).
