(hyperbolic) symmetry groups

mnb96

Hello,
how do symmetry groups in the Euclidean space differ from the symmetry groups in the hyperbolic space (in the Poincaré disk) ?
I've been told that in the hyperbolic case one has at disposal a richer "vocabulary" to describe symmetries, but I don't see how, and maybe I misunderstood.

Can anyone give me a hint and/or some source?
Thanks

mnb96	(hyperbolic) symmetry groups Hello, how do symmetry groups in the Euclidean space differ from the symmetry groups in the hyperbolic space (in the Poincaré disk) ? I've been told that in the hyperbolic case one has at disposal a richer "vocabulary" to describe symmetries, but I don't see how, and maybe I misunderstood. Can anyone give me a hint and/or some source? Thanks