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How to sew a three-holed cloth torus

It's obvious how to sew one-holed or two-holed tori. This page treats the three-holed torus.

A one-holed torus arises by identifying a rectangle's sides, a two-holed torus arises by identifying an octagon's sides. Then it's not surprising that a three-holed torus arises by identifying a dodecagon's sides in the following way.

[edge identifications]

The used tools:

Construct (or draw) and then cut the dodecagon:

[dodecagon]

A lot of sewing has to be done but after the first hole ...

[torus, one hole sewed]

... it's a short way to the three-holed cloth torus:

[the finished torus with three tapes]

[the finished torus]


For friends of jpegs: the little 3-holed-cloth-torus-gallery.


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