are all polyhedra that are not self-intersecting spherical?

Question

I know that Euler's Polyhedron formula $V-E+F=2$ applies to all spherical polyhedra.

I am working on a problem of reconstruction of polyhedra that have no self-intersections and I'd like to know whether or not all such polyhedra are spherical, so that I may use the formula

Answer 1

Consider any quadriangulation (or triangulation if you like) of a torus. That will be a polyhedron without self-intersections. But it will not be spherical: in fact, it has a hole.

--- rk