  This paper investigates the geometric structures and properties of
8-dimensional manifolds with Spin(7)-holonomy. We focus on the characterization
and implications of 4-planes within these manifolds, which are endowed with an
almost symplectic structure compatible with the Spin(7)-structure. We provide a
detailed analysis of the differential forms defining these structures,
including the Cayley 4-form and its stabilization under the Spin(7) group
actions. Furthermore, we explore the concept of mirror duality within the
context of exceptional holonomy, elucidating the relationship between dual
structures and their topological constraints. By examining the conditions under
which mirror duality arises, we enhance the understanding of the interplay
between Spin(7)-structures and symplectic geometry. This endeavor contributes
to our deeper understanding of the intricate symmetries and topological
properties of these remarkable manifolds.
