New York Journal of Mathematics
Volume 6 (2000) 237-283


S. Allen Broughton, Dawn M. Haney, Lori T. McKeough, and Brandy Smith Mayfield

Divisible Tilings in the Hyperbolic Plane

Published: October 4, 2000
Keywords: tiling, Fuchsian groups, reflection groups, crystallographic groups, hyperbolic plane
Subject: 05B45, 29H10, 20H15, 51F15, 52C20, 51M10

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 divisible tiling. All possible such divisible tilings are classified. There are a finite number of 1, 2, and 3 parameter families as well as a finite number of exceptional cases.


The last three authors were supported by NSF grant DMS-9619714

Author information

S. Allen Broughton:
Rose-Hulman Institute of Technology, Terre Haute IN, 47803

Dawn M. Haney:
University of Georgia, Athens, GA 30602

Lori T. McKeough:
St. Paul's School, Concord NH

Brandy Smith Mayfield:
3302 Cheyenne Court, Fairfield Twp, OH 45011