  Denote by $Sof(G)$ the space of sofic representations of a countable group
$G$. This space is known by a result of the second author, to have a
convex-like structure. We show that, in this space, minimal faces are extreme
points. We then construct uncountable many extreme points for
$Sof(\mathbb{F}_2)$ and show that there exists a decreasing chain of closed
faces with empty intersection. Finally we construct a strangely looking sofic
representation in $Sof(\mathbb{F}_2)$ that we believe it is outside of the
closure of the convex hull of extreme points.
