Abstract
A disc in \({{\mathbb R}^2}\) is called self-affine if it can be dissected into m ≥ 2 affine images of itself. We show that every self-affine convex disc D is a polygon. As a corollary, it turns out that D must be a triangle, a quadrangle or a pentagon.
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Dedicated to Prof. Dr. Eike Hertel on the occasion of his 70th birthday.
This research was supported by DFG grant RI 1087/3.
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Richter, C. Self-affine convex discs are polygons. Beitr Algebra Geom 53, 219–224 (2012). https://doi.org/10.1007/s13366-011-0044-8
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DOI: https://doi.org/10.1007/s13366-011-0044-8