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. Allen; Haney, Dawn M.; McKeough, Lori T.; and Smith, Brandy M., "Divisible Tilings in the Hyperbolic Plane" (2006). Faculty Publications - Mathematics. 16.