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Unpublished Paper
Triangular Surface Tiling Groups for Low Genus
Mathematical Sciences Technical Reports (MSTR)
  • Sean A Broughton, Rose-Hulman Institute of Technology
  • Robert M Dirks, Rose-Hulman Institute of Technology
  • Maria Sloughter, Rose-Hulman Institute of Technology
  • C. Ryan Vinroot, Rose-Hulman Institute of Technology
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Publication Date
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S. Allen Broughton
Consider a surface, S, with a kaleidoscopic tiling by non-obtuse triangles (tiles), i.e., each local reflection in a side of a triangle extends to an isometry of the surface, preserving the tiling. The tiling is geodesic if the side of each triangle extends to a closed geodesic on the surface consisting of edges of tiles. The reflection group G*, generated by these reflections, is called the tiling group of the surface. This paper classifies, up to isometry, all geodesic, kaleidoscopic tilings by triangles, of hyperbolic surfaces of genus up to 13. As a part of this classification the tiling groups G* are also classified, up to isometric equivalence. The computer algebra system Magma is used extensively.

MSTR 01-01

Citation Information
Sean A Broughton, Robert M Dirks, Maria Sloughter and C. Ryan Vinroot. "Triangular Surface Tiling Groups for Low Genus" (2001)
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