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$\mathbb{H}^{n}$ and Covolumes of Higher Dimensional Modular Groups
Higher dimensional analogues of the modular group 
$\mathit{PSL}(2,\mathbb{Z})$ are closely related to hyperbolic reflection groups and Coxeter polyhedra with big symmetry groups. In this context, we develop a theory and dissection properties of ideal hyperbolic 
$k$-rectified regular polyhedra, which is of independent interest. As an application, we can identify the covolumes of the quaternionic modular groups with certain explicit rational multiples of the Riemann zeta value 
$\unicode[STIX]{x1D701}(3)$.
In this paper we present new explicit simultaneous rational approximations which converge subexponentially to the values of the Bell polynomials at the points 
where m=1,2,…,a, a∈ℕ, γ is Euler’s constant and ζ is the Riemann zeta function.
