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

Divisible Tilings in the Hyperbolic Plane

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

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 \emph{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