There might be an English translation of Vigneras book. If not, at least three is [Arithmetic of Hyperbolic 3-manifolds](http://www.springer.com/gb/book/9780387983868) by Colin McLachlan and Alan Reid.  That book has information about quaternion algebras.  

I'll look into discussion of the fundamental volume of the tiling over $\mathbb{H}^3$.

In Chapter 11 they discuss Tamagawa measure.  If $A$ is a quaternion algebra,  and $\mathcal{O} \subseteq A $ is a maximal order then we've got a formula for the volume: 

$$\text{Vol}( SL(2,\mathbb{C})  / \rho (\mathcal(O)  )=
\frac{|\Delta|^{3/2}\zeta_k(2)\prod_{\mathcal(P)|N(A)}\big( N(\mathcal(P)-1\big)}
{(4\pi^2)^{[k:\mathbb{Q}]-2}}$$