S. Allen Broughton
In this paper, we consider triangle-quadrilateral pairs in the hyperbolic plane which “kaleidoscopically” tile the plane simultaneously. These tilings are called divisible tilings or subdivided tilings. We restrict our attention to the simplest case of divisible tilings, satisfying the corner condition, in which a single triangle occurs at each vertexof the quadrilateral. All possible such divisible tilings are catalogued as well as determining the minimal genus surface on which the divisible tiling exists. The tiling groups of these surfaces are also determined.
Haney, Dawn M. and McKeough, Lori T., "Quadrilaterals Subdivided by Triangles in the Hyperbolic Plane" (1998). Mathematical Sciences Technical Reports (MSTR). 111.