Split buildings of type F₄ in buildings of type E₆

A symplectic polarity of a building of type is a polarity whose fixed point structure is a building of type containing residues isomorphic to symplectic polar spaces (i.e., so-called split buildings of type ). In this paper, we show in a geometric way that every building of type contains, up to conjugacy, a unique class of symplectic polarities. We also show that the natural point-line geometry of each split building of type fully embedded in the natural point-line geometry of arises from a symplectic polarity