Genus-three surface

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"3-torus" redirects here. For the three-dimensional space, see Three-torus.

In geometry, a genus-three surface is 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. It is sometimes called the triple torus.

Klein quartic[edit]

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

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