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 of the quartic.
showed that this manifold is arithmetic.
