  We bootstrap the symbol of the maximal-helicity-violating four-particle form
factor for the chiral part of the stress-tensor supermultiplet in planar
$\mathcal{N}=4$ super-Yang-Mills theory at two loops. When minimally
normalized, this symbol involves only 34 letters and obeys the extended
Steinmann relations in all partially-overlapping three-particle momentum
channels. In addition, the remainder function for this form factor exhibits an
antipodal self-duality: it is invariant under the combined operation of the
antipodal map defined on multiple polylogarithms -- which reverses the order of
the symbol letters -- and a simple kinematic map. This self-duality holds on a
four-dimensional parity-preserving kinematic hypersurface. It implies the
antipodal duality recently noticed between the three-particle form factor and
the six-particle amplitude in this theory.
