How to sew a two-holed cloth torus

1. The one-holed Torus

It's well known that a one-holed torus (doughnut) results from identifying a rectangle's opposite sides: by sewing the horizontal edges we get a tube and by sewing the vertical edges (which mutated to circles) we get a torus.

2. The two-holed Torus

But how can we make a two-holed torus? Theoretically one gets a two-holed torus by identifying an octagon's edges in the following way:

[octagon with arrows]

But in nature? ... Let's try it. One needs the following things.

Construct (or draw) and then cut the octagon:

[a cloth octagon]

And now: sewing, ... (after the second seam emerges a topological pair of trousers) ...

Stop ...,
don't forget the stuffing!!

[sewed torus with one hole and two punctures]

The last seam ... Ready! The two-holed cloth torus:

[sewed two-holed torus]

By the way, you can use this needlework as a strange two-hands mitten.

The three-holed cloth torus

And now ... "We sew a three-holed cloth torus".

Sascha Rogmann (wwwmath@rogmann.org)
1996-07-14, last modified: 2001-03-12