Finding points of intersections between contours and mesh functions in ContourPlot3D

I have this code example that finds plane of zero first derivatives – the intersections of these planes will give the locations of the local extrema. Or at least a good starting point to finding them.

IIges2[x_, y_, z_] := Sin[x]^2 + Sin[y]^2 + Sin[z]^2;
xm = 4;

{dx[x_, y_, z_], dy[x_, y_, z_], dz[x_, y_, z_]} = 
  D[IIges2[x, y, z], {{x, y, z}}];

ccc = ContourPlot3D[{dx[x, y, z], dy[x, y, z], dz[x, y, z]} == 
   0, {x, -xm, xm}, {y, -xm, xm}, {z, -xm, xm}, ContourStyle -> None, 
  Mesh -> {{0}}, 
  MeshFunctions -> {dx[#, #, #] &, dy[#, #, #] &, dz[#, #, #] &}]

I can do

Cases[Normal@ccc, Line[x_] :> x, [Infinity]] 

to get the points along these lines of intersections. But how do I get the single points of intersections among all the lines?