Simpler formula for polyhedra with holes:

The number of holes in a polyhedra is called its genus. For a surface of genus p, F - E + V = 2 - 2p.

Source: http://www.cut-the-knot.org/do_you_know/polyhedra.shtml

Yes, holes through the polyhedron like in a torus.
I was just clarifying the AP's "If I recall correctly" formula.
Euler's rule for graphs (Nodes + Regions = Arcs + 2) only applies to graphs drawn on a plane as well, graphs drawn on toruses [edit: that pass through the hole] break that rule also.
Topology is an interesting topic, I found it very hard though. Maybe I shouldn't have skived all my lectures all those years ago.

Quote:Original post by Dmytry
Proven . Number of edges =(number of triangles * 3) / 2
So number of triangles must be even(otherwise we have non-integer number of edges), no matter if it's convex or not, it only need to be closed.

That's actually why I've posted...I came to the conclusion on my own (although probably everybody here on this forum already knew this) that to get the number of edges you multiply the number of triangles by 1.5, or 3/2, but only if the model is convex, and the number of triangles must always be even

EDIT:
and, like I said, I only care about convex models (so I can do things like run the brush algorithm on a transformed model for collision detection, stencil shadows, etc)