  We re-prove the classification of flexible octahedra, obtained by Bricard at
the beginning of the XX century, by means of combinatorial objects satisfying
some elementary rules. The explanations of these rules rely on the use of a
well-known creation of modern algebraic geometry, the moduli space of stable
rational curves with marked points, for the description of configurations of
graphs on the sphere. Once one accepts the objects and the rules, the
classification becomes elementary (though not trivial) and can be enjoyed
without the need of a very deep background on the topic.
