Divisible Tilings in the Hyperbolic Plane

Abstract:

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

S. Allen Broughton:
Rose-Hulman Institute of Technology, Terre Haute IN, 47803
allen.broughton@rose-hulman.edu
http://www.rose-hulman.edu/~brought/

Dawn M. Haney:
University of Georgia, Athens, GA 30602
haneydaw@arches.uga.edu

Lori T. McKeough:
St. Paul's School, Concord NH
lmckeoug@sps.edu

Brandy Smith Mayfield:
3302 Cheyenne Court, Fairfield Twp, OH 45011
brandymayfield@hotmail.com