Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Mathematics
Triangular Surface Tiling Groups For Low Genus, Sean A. Broughton, Robert M. Dirks, Maria Sloughter, C. Ryan Vinroot
Triangular Surface Tiling Groups For Low Genus, Sean A. Broughton, Robert M. Dirks, Maria Sloughter, C. Ryan Vinroot
Mathematical Sciences Technical Reports (MSTR)
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 …
Quest For Tilings On Riemann Surfaces Of Genus Six And Seven, Robert Dirks, Maria Sloughter
Quest For Tilings On Riemann Surfaces Of Genus Six And Seven, Robert Dirks, Maria Sloughter
Mathematical Sciences Technical Reports (MSTR)
The problem of kaleidoscopically tiling a surface by congruent triangles is equivalent to finding groups generated in certain ways. In order to admit a tiling, a group must have a specific set of generators as well as an involutary automorphism, T, that acts to reverse the orientation of the tiles. The purpose of this paper is to explore group theoretic and computational methods for determining the existence of symmetry groups and tiling groups, as well as to classify the symmetry and tiling groups on hyperbolic Riemann surfaces of genus 6 and 7.
Tilings Which Split A Mirror, Jim Belk
Tilings Which Split A Mirror, Jim Belk
Mathematical Sciences Technical Reports (MSTR)
We consider the mirror of a reflection which consists of its subset of fixed points. We investigate a number of conditions on the tiling that guarantee that the surface splits at a mirror.