I've been working with the hyperbolic plane quite a bit lately, and I've run across a few difficult questions I can't find the answers for.

First, I know that a regular polygon in the hyperbolic plane has to be constructed with a specific radius to be able to tessellate, and I've found a formula that works, but I haven't found any explaination for it.

Second, I've found a way of describing a translation in the hyperbolic plane by using a specific pair of reflections (this should work in any space where perpendicular is well defined) but is there an easier way?

I'll probably have some other questions later. Thanks.