Abstract
Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the x-axis, we look at the problem of the location of the vertices for a tiling of the polygon using lattice triangles (i.e., triangles which are congruent to a triangle with the coordinates of the vertices being integer). We show that the coordinates of the vertices in any tiling are rationals with the possible denominators odd numbers dependent on the cotangents of the angles in the triangles.
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S. Butler was supported by an NSF postdoctoral fellowship.
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Butler, S., Chung, F., Graham, R. et al. Tiling Polygons with Lattice Triangles. Discrete Comput Geom 44, 896–903 (2010). https://doi.org/10.1007/s00454-010-9249-0
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DOI: https://doi.org/10.1007/s00454-010-9249-0