S. Allen Broughton
In contribution to the classification of all tilings of low-genus surfaces, the kaleidoscopic and non-kaleidoscopic tilings by quadrilaterals are given up to genus 12. As part of their classification, the algebraic structure of the conformal tiling groups and the geometric structure of the tiles are specified. In addition, several infinite classes of tilings and tiling groups are presented.
Gregoire, John and Averil, Isabel, "Tilings of Low-Genus Surfaces by Quadrilaterals" (2002). Mathematical Sciences Technical Reports (MSTR). 94.