Everyone knows that it's difficult to compute a general fundamental domain for an arithmetic group but are there any specific examples where such domains have been calculated? I'm mostly interested in results related to orthogonal groups of lattices of type O(2, n).

I've only really been able to track down two such results:

Vinberg's algorithm computes a fundamental domain for reflective groups of type O(1,n); and Gottschling was able to compute a Minkowski reduced domain for the integral symplectic group Sp(4, Z), which can be considered of type O(2, 3).

Would the situation improve if one were to study fundamental domains of p-groups?

Everyone knows that it's difficult to compute a general fundamental domain for an arithmetic group but are there any specific examples where such domains have been calculated? I'm mostly interested in results related to orthogonal groups of lattices of type O(2, n).

I've only really been able to track down two such results:

Vinberg's algorithm computes a fundamental domain for reflective groups of type O(1,n); and Gottschling was able to compute a Minkowski reduced domain for the integral symplectic group Sp(4, Z), which can be considered of type O(2, 3).

Would the situation improve if one were to look at a restricted problem, and study fundamental domains of groups generated by p-torsion, for example?

Everyone knows that it's difficult to compute a general fundamental domain for an arithmetic group but are there any specific examples where such domains have been calculated? I'm mostly interested in results related to orthogonal groups of lattices of type O(2, n).

I've only really been able to track down two such results:

Vinberg's algorithm computes a fundamental domain for reflective groups of type O(1,n); and Gottschling was able to compute a Minkowski reduced domain for the symplectic group Sp(4), which can be considered of type O(2, 3).

Would the situation improve if one were to study fundamental domains of p-groups?

Everyone knows that it's difficult to compute a general fundamental domain for an arithmetic group but are there any specific examples where such domains have been calculated? I'm mostly interested in results related to orthogonal groups of lattices of type O(2, n).

I've only really been able to track down two such results:

Vinberg's algorithm computes a fundamental domain for reflective groups of type O(1,n); and Gottschling was able to compute a Minkowski reduced domain for the integral symplectic group Sp(4, Z), which can be considered of type O(2, 3).

Would the situation improve if one were to study fundamental domains of p-groups?