Real Projective Plane with One Handle:

Alternatively, it is the connected sum of a real projective plane with a torus. Less formally, it is a projective plane with two disks removed and a tube inserted between the two disks. This is demonstrated in the diagram below:

This is the triangulation of the projective plane with one handle used to build the tight polyhedral immersion presented here . The two removed disks are shown in grey, and the tube is shown at the right. The dotted line is the double curve of the tight immersion.