Tilings which Split a Mirror
Jim Belk · Rose-Hulman Scholar (Rose–Hulman Institute of Technology) · 1999
Let φ be a reflection on a surface Σ. The mirror of φ is the fixed point subset Σφ = {x ∈ Σ:φ(x) =x}, which is a disjoint union of circles. We say that Σ splits at the mirror of φ if Σ−Σφ is disconnected. We further assume that the reflection is a symmetry of a tiling of Σ by triangles. In this paper we investigate a number of conditions on the