  The $\bar{Q}$ equations, rooted in the dual superconformal anomalies, are a
powerful tool for computing amplitudes in planar $\mathcal{N}=4$ supersymmetric
Yang-Mills theory. By using the $\bar{Q}$ equations, we compute the symbol of
the first MHV amplitude with algebraic letters -- the three-loop 8-point
amplitude (or the octagon remainder function) -- in this theory. The symbol
alphabet for this amplitude consists of 204 independent rational letters and
shares the same 18 algebraic letters with the two-loop 8-point NMHV amplitude.
