TITLE: Escher, Conway,  Kali, etc.
QUESTION [7 upvotes]: One can express the symmetry types of, say, Escher's "Circle Limit" prints using
Conway's orbifold notation, best known in the context of symmetries of Euclidean
plane patterns.  
For example, Circle Limit III has symmetry type $433$ (with Euler characteristic $-1/12$).
Where can I find an explicit algorithm that produces generators for some appropriate 
subgroup of the isometries of the Poincaré model of the hyperbolic plane given a suitable Conway notation?  Only certain notation give rise to rigid orbifolds, so I'd also like
to know how to read off the number of moduli from the Conway notation.  Absent rigidity,
I'd really like a parametric family of generating sets realizing all the distinct forms of
the underlying orbifold.
The popular program Kali facilitates drawing symmetric Euclidean patterns?  Does anyone
distribute some appropriate hyperbolic counterpart?

REPLY [2 votes]: Can't speak for the Conway -> generators, but for drawing, there is this
http://www.plunk.org/~hatch/HyperbolicApplet/
I am not sure why "rummaging" was necessary for the D. Huson program, since there is a link to it on the "OrbifoldNotation" wikipedia page.