Meyerhoff manifold

In hyperbolic geometry, the Meyerhoff manifold is the arithmetic hyperbolic 3-manifold obtained by $$(5,1)$$ 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
 * $$V_m = 12\cdot(283)^{3/2}\zeta_k(2)(2\pi)^{-6} = 0.981368\dots$$

of orientable arithmetic hyperbolic 3-manifolds, where $$\zeta_k$$ is the zeta function of the quartic field of discriminant $$-283$$. Alternatively,


 * $$V_m = \Im(\rm{Li}_2(\theta)+\ln|\theta|\ln(1-\theta)) = 0.981368\dots$$

where $$\rm{Li}_n$$ is the polylogarithm and $$|x|$$ is the absolute value of the complex root $$\theta$$ (with positive imaginary part) of the quartic $$\theta^4+\theta-1=0$$.

showed that this manifold is arithmetic.