SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\PlanetHopf"];
<< PlanetHopf-Programs.m

LoadColourScheme["101127-222611"]

MakeImage["DiskMap", Graphics[{
EdgeForm[Black],Circle[{0,0},1], Circle[{0,0},1],
{
Hue[CountryColour[#]],
CountryShape[#] 
/. LonLat[lon_, lat_] :> (s=sigma[LonLat[lon, -lat]][[1]]; s={Re[s], Im[s]}; s)
/. {CountryShape  -> List, Region[pts___] :> Polygon[{pts}]}
}& /@ 
AllCountries
}]]