In practice, most wavefront-obj faces are coplanar and convex, but I can't find anything in the original OBJ specification saying this is guaranteed.
If the face is coplanar and convex, you can either use GL_TRIANGLE_FAN, or you can use GL_TRIANGLE and manually evaluate the fan yourself. A fan has all triangles share the first vertex. Like this:
// manually generate a triangle-fan
for (int x = 1; x < (faceIndicies.Length-1); x++) {
renderIndicies.Add(faceIndicies[0]);
renderIndicies.Add(faceIndicies[x]);
renderIndicies.Add(faceIndicies[x+1]);
}
If the number of vertices in an n-gon is large, using GL_TRIANGLE_STRIP, or manually forming your own triangle strips, can produce better visual results. But this is very uncommon in wavefront OBJ files.
If the face is co-planar but concave, then you need to triangulate the face using an algorithm, such as the Ear-Clipping Method..
http://en.wikipedia.org/wiki/Polygon_triangulation#Ear_clipping_method
If the verticies are not-coplanar, you are screwed, because OBJ doesn't preserve enough information to know what shape tessellation was intended.
GL_POLYGON
? I don't think that OBJs typically have concave polygons, if they do, you need to tessellate it first. For tessellating you can use the gluTesselator: glprogramming.com/red/chapter11.html – Maharanee