Wrong cloth collision of some faces only

I am a new Blender user and I would like to learn how to use cloth collisions.
My objective is to get a cloth plane to lay on a sphere and on other objects.

As you can see from the attached picture, I always get some faces of the plane to go through the sphere. It is happening always on four zones facing each other.
I tried to push the quality of collisions higher but it did not help.

Is there anything obvious that I am missing? or I just need to tune the collision parameters as long as I get rid of this problem?

I am using Blender 2.71.

Thank you very much


Does your plane have any thickness? Also, check out this tutorial where Andrew Price talks about cloth collsions: