Divisible Tilings in the Hyperbolic Plane
We consider triangle-quadrilateral pairs in the hyperbolic plane which “kaleidoscopically” tile the plane simultaneously.In this case the tiling by quadrilaterals is called a divisiblet iling.All possible such divisible tilings are classified. There are a finite number of1, 2, and 3 parameter families as well as a finite number of exceptional cases.
Broughton, S.A., Haney, D.M., McKeough, L.T., & Mayfield, B.S. (2000). Divisible tilings in the hyperbolic plane. In New York Journal of Mathematics, 6, 237-283.