  The purpose of this note is to define tri-moment maps for certain manifolds
that carry closed non-degenerate 4-forms and an $Sp(1)^n$-action. Examples
include quaternionic vector spaces and flag manifolds. We show how this map can
be used ro reduce such manifolds to the ones with fewer symmetries. The images
of such maps for quaternionic flag manifolds, which are defined using the
Dieudonn\'e determinant, resemble the polytopes from the complex case.
