Topology and Wings3D

[cyseal]

How to explain abstract shape in topological terms?

Basically,we start with a polyhedron. It's topologically equvialent to sphere.
If we inset and intrude all faces, we'll get surface of genus h, where h is a number of holes we got from intruding the faces.

For example, sphericon is also genus surface.

What does it happen with topology when we make an loop cuts or delete a face rings on a mesh?
How to categorize that mesh as a mathematical surface/manifold?