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# Triple torus

In the theory of surfaces, a triple torus refers to a smooth closed surface with three holes, or, in other words, a surface of genus three. It can be obtained by attaching three handles to a sphere or by gluing (taking the connected sum) of three tori.

A sphere with three handles, The connected sum of three tori, Pretzel-style triple torus

Dodecagon with opposite edges identified, Tetradecagon with opposite edges identified

Klein quartic

An example of a genus-3 Riemann surface is the Klein quartic.

See also

Double torus

Three-torus

External links

Weisstein, Eric W., "Triple Torus", MathWorld.

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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