All Questions

Consider generic configurations consisting of 4 distinct circles on the sphere. Two configurations are equivalent if they can be mapped onto each other by a homeomorphism of the sphere. How to ...

Is it known what the smallest tile (in terms of area) that can tessellate the hyperbolic plane is? In particular, it should tessellate the plane by itself. I think it will be a Triangle group, but I'...

Is there a smallest tile (in terms of diameter) that isohedrally tessellates the hyperbolic plane? In this question, we ask the same question without the isohedral requirement, and the answer was no. ...

Let $P$ be a hyperbolic $4n$ gon having opposite sides with equal length and the sum of all interior angles is $2\pi$. Then is true that opposite angles are equal also?