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 Robert Meyerhoff 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, Ted Chinburg showed that this manifold is arithmetic.