  The computation of a certain class of four-point functions of heavily charged
BPS operators boils down to the computation of a special form factor - the
octagon. In this paper, which is an extended version of the short note [1], we
derive a non-perturbative formula for the square of the octagon as the
determinant of a semi-infinite skew-symmetric matrix. We show that
perturbatively in the weak coupling limit the octagon is given by a determinant
constructed from the polylogarithms evaluating ladder Feynman graphs. We also
give a simple operator representation of the octagon in terms of a vacuum
expectation value of massless free bosons or fermions living in the rapidity
plane.
