Polygon with holes

An ordinary polygon can be called simply-connected, while a polygon-with-holes is multiply-connected.

[3] A polygons with holes can be transformed into an ordinary unicursal boundary path by adding (degenerate) connecting double-edges between boundaries, or by dissecting or triangulating it into 2 or more simple polygons.

The 1-skeleton (vertices and edges) of a polyhedron with holed-faces is not a connected graph.

Each set of connected edges will make a separate polyhedron if their edge-connected holes are replaced with faces.

A face with a degenerate digon hole adds 2 vertices and 2 coinciding edges, where the two edges attach to two coplanar faces, as a dihedron hole.

Polygons with holes, with simply connected brown regions and interior boundaries, including degenerate cases of single vertices and edges, (a,b,f).
Example conversion of a single-holed polygon by connecting edges, or dissection