In this talk, the computation of the covolume of the group of units of the
quadratic form

$$x_1^2+x_2^2+\cdots +x_n^2-d\hspace{.01in}x_{n+1}^2$$

with $d$ an odd, square-free, positive integer, will be described.
The covolume will be expressed in terms of Bernoulli numbers, Dirichlet $L$-functions, and powers of $\pi$.

John Mcleod has recently determined the hyperbolic Coxeter fundamental domain of the reflection subgroup of the group
of units for the case $d = 3$.
We apply our covolume formula to determine the volumes of Mcleod's hyperbolic Coxeter polytopes.

[invited by R. Kellerhals]