S. Allen Broughton
The problem of kaleidoscopically tiling a surface by congruent triangles is equivalent to finding groups generated in certain ways. In order to admit a tiling, a group must have a specific set of generators as well as an involutary automorphism, T, that acts to reverse the orientation of the tiles. The purpose of this paper is to explore group theoretic and computational methods for determining the existence of symmetry groups and tiling groups, as well as to classify the symmetry and tiling groups on hyperbolic Riemann surfaces of genus 6 and 7.
Dirks, Robert and Sloughter, Maria, "Quest for Tilings on Riemann Surfaces of Genus Six and Seven" (2000). Mathematical Sciences Technical Reports (MSTR). 101.