Boolean modifier just remove my object I wanted to apply a modifier between two cones. Here is what you can see before I make it visible:

and after:

As you can see, the bigger cone just disapeared. I tried to update the normals (Shift-N in edit mode or Mesh &gt; Normal &gt; Recalculate outside) of both the small and the large cone, still the same issue. Actually, the cone disappear even if I use union!
Also, to make sure that the pointy vertex is not removed, I made sure to shift a bit the smaller cone:

Here is the file: http://www.filedropper.com/01problememodifier
-- EDIT --
I also tried to intersect these two shapes:

and here is the result (fast mode):

In exact mode, I see nothing... but if I click on self, it works!
I turns out that I just need to click on &quot;self&quot; on the modifer, no idea why it's not checked by default:

EDIT: as pointed out in the comment, the problem may be instead that the shape had double vertices (created when I turned the cylinder into a cone by scaling one side). Therefore, it may also be enough to remove doubles vertices (Edit mode &gt; Mesh &gt; Merge &gt; By distance), thanks!