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A quadruple torus is a topological surface with four holes, formed from the connected sum of four tori. It has an orientable genus of 4[1] and an Euler characteristic of -6[2].

Structure and Sections

All orientable manifolds with four holes (i.e. with an Euler characteristic of -6) are homeomorphic to the quadruple torus due to the classification theorem of closed surfaces[3].

See Also

\mathbb{S}^2 \mathbb{T}^2 2\mathbb{T}^2 3\mathbb{T}^2 4\mathbb{T}^2
Sphere Torus Double torus Triple torus Quadruple torus

References

  1. http://mathworld.wolfram.com/Genus.html
  2. http://mathworld.wolfram.com/EulerCharacteristic.html
  3. http://en.wikipedia.org/wiki/Surface_(topology)#Classification_of_closed_surfaces

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