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Full-Text Articles in Mathematics
Symmetry And Tiling Groups For Genus 4 And 5, C. Ryan Vinroot
Symmetry And Tiling Groups For Genus 4 And 5, C. Ryan Vinroot
Mathematical Sciences Technical Reports (MSTR)
All symmetry groups for surfaces of genus 2 and 3 are known. In this paper, we classify symmetry groups and tiling groups with three branch points for surfaces of genus 4 and 5. Also, a class of symmetry groups that are not tiling groups is presented, as well as a class of odd order non-abelian tiling groups.
Quadrilaterals Subdivided By Triangles In The Hyperbolic Plane, Dawn M. Haney, Lori T. Mckeough
Quadrilaterals Subdivided By Triangles In The Hyperbolic Plane, Dawn M. Haney, Lori T. Mckeough
Mathematical Sciences Technical Reports (MSTR)
In this paper, we consider triangle-quadrilateral pairs in the hyperbolic plane which “kaleidoscopically” tile the plane simultaneously. These tilings are called divisible tilings or subdivided tilings. We restrict our attention to the simplest case of divisible tilings, satisfying the corner condition, in which a single triangle occurs at each vertexof the quadrilateral. All possible such divisible tilings are catalogued as well as determining the minimal genus surface on which the divisible tiling exists. The tiling groups of these surfaces are also determined.