Meyerhoff manifold
In hyperbolic geometry, the Meyerhoff manifold is the arithmetic hyperbolic 3-manifold obtained by formula_1 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 formula_3 is the zeta function of the quartic field of discriminant formula_4. Alternatively, where formula_6 is the polylogarithm and formula_7 is the absolute value of the complex root formula_8 (with positive imaginary part) of the quartic formula_9