Geodesic
Dissecting a square into congruent polygons
Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 1.

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We study the dissection of a square into congruent convex polygons. Yuan \emph{et al.} [Dissecting the square into five congruent parts, Discrete Math. \textbf{339} (2016) 288-298] asked whether, if the number of tiles is a prime number $\geq 3$, it is true that the tile must be a rectangle. We conjecture that the same conclusion still holds even if the number of tiles is an odd number $\geq 3$. Our conjecture has been confirmed for triangles in earlier works. We prove that the conjecture holds if either the tile is a convex $q$-gon with $q\geq 6$ or it is a right-angle trapezoid.
DOI : 10.23638/DMTCS-22-1-21
Classification : 05B45, 05C45, 52C20 
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Rao, Hui; Ren, Lei; Wang, Yang. Dissecting a square into congruent polygons. Discrete mathematics & theoretical computer science, Tome 22 (2020-2021) no. 1. doi : 10.23638/DMTCS-22-1-21. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-22-1-21/

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