Weeks manifold

Example

Take the complement of the Whitehead link in $S^3$. The Weeks manifold $W$ is the closed orientable $3$-manifold obtained from it by Dehn filling with coefficients $(5, 1)$ and $(5, 2)$ on the two components. It is a closed hyperbolic 3-manifold. Its hyperbolic volume is approximately $0.9427$. Its first homology group is $H_1(W; \Z) \cong \Z/5 \oplus \Z/5$.

The hyperbolic structure can be checked by computer, for example with the program SnapPea of Jeffrey Weeks.