I vaguely remember seeing something in OpenGL (not ES, which was still at v1.0 on the iPhone when I came across this, which is why I never used it) that let me specify which edges of my polygons were considered outlines vs those that made up the interior of faces. As such, this isn't the same as the outline of the entire model (which I know how to do), but rather the outline of a planar face with all its tris basically blended into one poly. For instance, in a cube made up of tri's, each face is actually two tris. I want to render the outline of the square, but not the diagonal across the face. Same thing with a hexagon. That takes four tris, but just one outline for the face.
Now yes, I know I can simply test all the edges to see if they share coplanar faces, but I could have sworn I remember seeing somewhere when you're defining the tri mesh data where you could say 'this line outlines a face whereas this one is inside a face.' That way when rendering, you could set a flag that basically says 'Give me a wireframe, but only the wires around the edges of complete faces, not around the tris that make them up.'
BTW, my target is all platforms that support OpenGL ES 2.0 but my dev platform is iOS. Again, this Im pretty sure was originally in OpenGL and may have been depreciated once shaders came on the scene, but I can't even find a reference to this feature to check if that's the case.
The only way I know now is to have one set of vertices, but two separate sets of indices... one for rendering tris, and another for rendering the wireframes of the faces. It's a real pain since I end up hand-coding a lot of this, which again, I'm 99% sure you can define when rendering the lines.
GL_QUADS, glEdgeFlag and glPolygonMode are not supported in OpenGL ES.
You could use LINES to draw the wireframe: To get hidden lines, first draw black filled triangles (with DEPTH on) and then draw the edges you are interested in with GL_LINES.