Ok, some words to cones with sharp tip.
Although mathematically well defined leads such a cone
to some problems in Brep data
structures. A surface come together in one infinite small point at the top. Such a geometry will
always leads to problems. the mesher, which produce that visual artifacts you see, e.g can not
decide at the tip what surface normal he have to use for the triangles at that point. also quit sure
some modeling algorithms will fail at that tip.
don't do it!
Use a small plane at the top or think of something else....