ho.history overview - Do there exist modern expositions of Klein's Icosahedron?

In my PH Thesis work
http://systembit.es/schwarz.htm

In my papier I have asociatted a Riemann Surface to each Schwarz function triangle.
After that ,I´ve got genus and geometric density of spherical tesselation expresions in a new method.
Then I see Their Poincare Groups ( of each above Riemann Surfaces) as index normal finite subgroup of Г(2) (Thanks to Modular Function Lambda).
Then I calculate signature of these fuchisian Groups.
Finally I see there are only nine ( of above Riemann Surfaces) more Dihedrical cases.

I think my idea is a new interpretation of Schwarz triangles , different one to the Famous Schwarz Classification based on 14 Schwarz triangles +Dihedrical cases.

Alfonso García
alfonso@systembit.es