Genus-three surface

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.

• Several representations of the genus-three surface
• 
  A sphere with three handles
• 
  The connected sum of three tori
• 
  Triple torus
• 
  Dodecagon with opposite edges identified
• 
  Tetradecagon with opposite edges identified

Klein quartic

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

See also

• Torus
• Genus-two surface
• Three-torus

External links

• Weisstein, Eric W.. "Triple Torus". http://mathworld.wolfram.com/TripleTorus.html.