episciences.org_6022_1675654280 1675654280 episciences.org raphael.tournoy+crossrefapi@ccsd.cnrs.fr episciences.org Discrete Mathematics & Theoretical Computer Science 1365-8050 06 29 2020 vol. 22 no. 1 Combinatorics Dissecting a square into congruent polygons Hui Rao Lei Ren Yang Wang 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. 06 29 2020 6022 https://arxiv.org/licenses/nonexclusive-distrib/1.0 arXiv:2001.03289 10.48550/arXiv.2001.03289 https://arxiv.org/abs/2001.03289v2 https://arxiv.org/abs/2001.03289v1 10.23638/DMTCS-22-1-21 https://dmtcs.episciences.org/6022 https://dmtcs.episciences.org/6596/pdf https://dmtcs.episciences.org/6596/pdf