  We study the antipodal subsets of the full flag manifolds
$\mathcal{F}(\mathbb{R}^d)$. As a consequence, for natural numbers $d \ge 2$
such that $d\ne 5$ and $d \not\equiv 0,\pm1 \mod 8$, we show that Borel Anosov
subgroups of ${\rm SL}(d,\mathbb{R})$ are virtually isomorphic to either a free
group or the fundamental group of a closed hyperbolic surface. This gives a
partial answer to a question asked by Andr\'es Sambarino. Furthermore, we show
restrictions on the hyperbolic spaces admitting uniformly regular
quasi-isometric embeddings into the symmetric space $X_d$ of ${\rm
SL}(d,\mathbb{R})$.
