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Full-Text Articles in Mathematics
Splitting Tiled Surfaces With Abelian Conformal Tiling Group, Sean A. Broughton
Splitting Tiled Surfaces With Abelian Conformal Tiling Group, Sean A. Broughton
Mathematical Sciences Technical Reports (MSTR)
Let p be a reflection on a closed Riemann Surface S, i.e., an anti-conformal involutary isometry of S with a non-empty fixed point subset. Let Sp denote the fixed point subset of p, which is also called the mirror of p. If S −Sp has two components, then p is called separating and we say that S splits at the mirror Sp. Otherwise p is called non-separating. We assume that the system of mirrors, Sq, as q varies over all reflections in the isometry group Aut*(S) defines a tiling of the surface, consisting of triangles. In turn, the tiling determines …
Divisible Tilings In The Hyperbolic Plane, Sean A. Broughton, Dawn M. Haney, Lori T. Mckeough, Brandy M. Smith
Divisible Tilings In The Hyperbolic Plane, Sean A. Broughton, Dawn M. Haney, Lori T. Mckeough, Brandy M. Smith
Mathematical Sciences Technical Reports (MSTR)
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.
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.
Automorphic Subsets Of The N-Dimensional Cube Are Translations Of Cwatsets, Matthew Lepinski
Automorphic Subsets Of The N-Dimensional Cube Are Translations Of Cwatsets, Matthew Lepinski
Mathematical Sciences Technical Reports (MSTR)
It is known that automorphic subsets are generalizations of cwatsets. In this paper we show that an automorphic subset is the translation of some cwatset, and therefore that each automorphic subset is internally isomorphic to a cwatset.