Abstract
A k-dissection D of a polygon P, is a partition of P into a set pf subpolygons {Q 1,...,Q m } with disjoint interiors such that these can be reassembled to form k polygons P 1,...,P k all similar to P. If for every j, 1 ≤ j ≤ k, the pieces of D can be assembled into j polygons, all similar to P, then D is called a sequentially k-divisible dissection. In this paper we show that any convex n-gon, n ≤ 5, has a sequentially k-divisible dissection with (k - 1)n+1 pieces. We give sequentially k-divisible dissections for some regular polygons with n ≥ 6 vertices. Furthermore, we show that any simple polygon P with n vertices has a (3k+4)-dissection with (2n - 2) +k(2n + ⌊ n/3 ⌋ - 4) pieces, k ≤ 0, that can be reassembled to form 4,7,..., or 3k + 4 polygons similar to P. We give similar results for star shaped polygons.
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© 2001 Springer-Verlag Berlin Heidelberg
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Akiyama, J., Sakai, T., Urrutia, J. (2001). Sequentially Divisible Dissections of Simple Polygons. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_4
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DOI: https://doi.org/10.1007/3-540-47738-1_4
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