# Maximum number of edges in a concave polyhedron given n vertices

Given $$n$$ vertices of a concave polyhedron (3D), what are the maximum amount of edges it can have?

I know for convex polyhedra the upper bound is $$3n-6$$. Does this also hold for concave polyhedra?

Also, if $$3n-6$$ edges is also the upper bound for concave polyhedra, is this due to the fact that every concave polyhedron can be represented as a planar graph?

It depends on how you define polyhedron. Do you allow "holes" like in a donut? While I have no answer to the case of general $$n$$ (this might be very hard), here is a polyhedron on $$n=7$$ vertices with the maximal number of
$${7\choose 2}=21 \;\text{ edges},$$
which is bigger than $$3n-6=15$$.