Rhombus shaped polyhedron, and a cylinder each render perfectly with F5
and F6

The two together render perfectly with F5 - but FAIL with F5

Points= [   [0, 5.90205, 2], [3.54123, 0, 2], [0, -5.90205, 2],
            [-3.54123, 0, 2], [-2.45877, 0, 2], [0, -4.09795, 2],
            [2.45877, 0, 2], [0, 4.09795, 2], [0, 6.94365, 0],
            [4.16619, 0, 0], [0, -6.94365, 0], [-4.16619, 0, 0],
            [-1.83381, 0, 0], [0, -3.05635, 0], [1.83381, 0, 0],
            [0, 3.05635, 0] ];
Faces =  [  [8, 9, 1], [9, 10, 2], [10, 11, 3], [8, 1, 0],
            [9, 2, 1], [10, 3, 2], [12, 13, 5], [13, 14, 6],
            [14, 15, 7], [12, 5, 4], [13, 6, 5], [14, 7, 6],
            [0, 7, 4],[0, 4, 3], [12, 15, 8],[12, 8, 11],
            [12, 4, 7], [12, 7, 15], [11, 3, 0], [11, 0, 8],
            [0, 1, 6],[0, 6, 7], [1, 2, 5],[1, 5, 6],
            [2, 3, 4],[2, 4, 5], [9, 8, 15],[9, 15, 14],
            [10, 9, 14],[10, 14, 13], [11, 10, 13],[11, 13, 12]];
//
polyhedron(Points,Faces,10);
translate([0,0,0])cylinder($fn=60,r=1,h=3);

Rendering Polygon Mesh using CGAL...

ERROR: The given mesh is not closed! Unable to convert to
CGAL_Nef_Polyhedron.

Turn on "Thrown Together" view.
Flip winding order (reverse points) of the face shown in pinkish color.

ciao,
Torsten.