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S. Allen Broughton, Dawn M. Haney, Lori T. McKeough, and Brandy Smith Mayfield
Divisible Tilings in the Hyperbolic Plane
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| Published: |
October 4, 2000 |
| Keywords: |
tiling, Fuchsian groups, reflection groups, crystallographic groups, hyperbolic plane |
| Subject: |
05B45, 29H10, 20H15, 51F15, 52C20, 51M10 |
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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 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.
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| Acknowledgements
The last three authors were supported by NSF grant DMS-9619714
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| Author information
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
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