  For a given divison algebra of the quaternions we construct two types of
units: Pell units and Gauss units. If K is a rational quadratic extension and G
is a finite group, we classify R and G, s.t., the unit group U(RG) of
augmentation one is hyperbolic. In particular we give necessary and sufficient
conditions when G is the quaternion group of order 8. In this case, the
hyperbolic boundary is isomorphic to the 2-dimensional sphere. As a result we
reach a class of groups of one end, that are not virtually free.
