  We provide a complete characterisation of extreme points of the space of
sofic representations. We also show that the restriction map
$Sof(G,P^{\omega})$ to $Sof(H,P^{\omega})$, where $H\subset G$ is not always
surjective. The first part of the paper is a continuation of [Pa2] and follows
more closely the plan of Nathanial Brown from [Br].
