  In this article we present the hexagon equations for dilogarithms which come
from the analytic continuation of the dilogarithm $\mathrm{Li}_2(z)$ to
${\mathbf P}^1 \setminus {0,1,\infty}$. The hexagon equations are equivalent to
the coboundary relations for a certain 1-cocycle of holomorphic functions on
${\mathbf P}^1$, and are solved by the Riemann-Hilbert problem of additive
type. They uniquely characterize the dilogarithm under the normalization
condition.
