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# 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:

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

- a 35x35 inē piece of cloth
- needle and thread
- to construct the octagon:
- a pair of compasses and a ruler --- or
- ruler, pocket calculator and a sheet of paper

- stuffing (the material in soft toys)
- a few hours of free time
- not necessary but helpful: Rachmaninov's First Piano Concerto

Construct (or draw) and then cut the octagon:

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

Stop ...,

don't forget the stuffing!!

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