I have this problem with blender. I have created a mesh consisting of around 400 vertices. In Cycles Render I added a Glass Shader and connected the "Generated" Output of the "Texture Coordinate" Node to the "Color" Input of the Glass Shader, because of this its pretty colorful. So the problem is, that if I render it there are those black rendered faces, as seen I have also put the Blender File on Google Drive, so you can look at it: click here.
Does anyone know how I can fix those faces?