Meyerhoff manifold
In hyperbolic geometry, the Meyerhoff manifold is the arithmetic hyperbolic 3-manifold obtained by  surgery on the figure-8 knot complement. It was introduced by  as a possible candidate for the hyperbolic 3-manifold of smallest volume, but the Weeks manifold turned out to have  slightly smaller volume. It has  the second smallest volume 

of orientable arithmetic hyperbolic 3-manifolds, where  is the zeta function of the quartic field of discriminant . Alternatively,

 

where  is the polylogarithm and  is the absolute value of the complex root  (with positive imaginary part) of the quartic . showed that this manifold is arithmetic. See also
Gieseking manifold
Weeks manifold

References

3-manifolds
Hyperbolic geometry