Even Number of Triangles for Any 3D model

[unknown]

Is it impossible for a 3D model to have an odd number of triangles?
Assuming its got every edge has two triangles.

[Zekaric]

If the surface is properly formed, no (I think); but if it has degenerate triangles, meaning two or more of a triangle's points are coincident, then all bets are off.

I'm still trying to think of a case where it may fail but I'm not finding it.