## FANDOM

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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].

$\mathbb{S}^2$ $\mathbb{T}^2$ $2\mathbb{T}^2$ $3\mathbb{T}^2$ $4\mathbb{T}^2$