  Let $\theta$ be an automorphism of a thick irreducible spherical building
$\Delta$ of rank at least $3$ with no Fano plane residues. We prove that if
there exist both type $J_1$ and $J_2$ simplices of $\Delta$ mapped onto
opposite simplices by $\theta$, then there exists a type $J_1\cup J_2$ simplex
of $\Delta$ mapped onto an opposite simplex by $\theta$. This property is
called "cappedness". We give applications of cappedness to opposition diagrams,
domesticity, and the calculation of displacement in spherical buildings. In a
companion piece to this paper we study the thick irreducible spherical
buildings containing Fano plane residues. In these buildings automorphisms are
not necessarily capped.
