Here 16 cylinders intersect following the corners of a rhombotriacontahedra.

With radius 1 the surface of the intersection is

12.6321

and its volume is a third of the surface.

We have four different not flat corners. The symmetric corner with three edges has a solid angle of 42.21%. The corner with three edges at the corner of the pentagons has a solid angle of 46.09%. This corner also exists in the icosahedral intersection of 6 cylinders. The corner with three edges in the concavity of the star has a solid angle of 45.88%. The corner with five edges has a solid angle of 39.69%. This corner also exists in the iintersection of 10 cylinders.

The surface S can be calculated with the following formulas: