  We view space-filling circle packings as subsets of the boundary of
hyperbolic space subject to symmetry conditions based on a discrete group of
isometries. This allows for the application of counting methods which admit
rigorous upper and lower bounds on the Hausdorff dimension of the residual set
of a generalized Apollonian circle packing. This dimension (which also
coincides with a critical exponent) is strictly greater than that of the
Apollonian packing.
