Here 19 cylinders intersect. 15 axis passe through the center of the edges of the dodecahedron and 4 through the corners of the cube inserted in the dodecahedron. Added 2.4.2009.

 

 

With radius 1 the surface of the intersection is

12.6112563

and its volume is a third of the surface.

 

The intersection has 336 facets.