Geodesic
On subdivisions of polygons
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 13, Tome 476 (2018), pp. 143-152 Cet article a éte moissonné depuis la source Math-Net.Ru

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By a subdivision of a polygon, we mean an orthogonal net such that the vertices of the polygon are nodes of the net, and the edges are composed of diagonals and sides of its cells. We study the subdivisions of convex polygons in which all edges have only diagonal directions. Such a polygon has four supporting vertices disposed on the different sides of the described rectangular. From each nonsupporting vertex, toward the interior of the polygon, there emanates a pair of broken lines in the directions of the orthogonal net. After a finite number of reflections in the boundary (the sum of the incidence and reflection angles is equal to $90^\circ$), the broken lines of such a pair can either get stuck at the supporting vertices or meet each other and form a closed orbit. It is proved that in the case of the pentagon, the second variant is not possible. 
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M. Yu. Nikanorova; Yu. R. Romanovski. On subdivisions of polygons. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 13, Tome 476 (2018), pp. 143-152. http://geodesic.mathdoc.fr/item/ZNSL_2018_476_a10/

[1] N. Yu. Dodonov, A. V. Masalskikh, “Rekonstruktsiya parametricheskikh poverkhnostei, zadannykh tablichno, posredstvom sdvigov i szhatii odnoi funktsii”, Izvestiya Tulskogo gosudarstvennogo universiteta. Estestvennye nauki, 2014, no. 1-1, 232–248

[2] N. Yu. Dodonov, A. V. Masalskikh, “Primenenie odnogo klassa agregatov priblizheniya summatornogo tipa dlya rekonstruktsii parametricheskikh poverkhnostei”, Izvestiya Tulskogo gosudarstvennogo universiteta. Estestvennye nauki, 2014, no. 2, 59–75

[3] N. Yu. Dodonov, “O ravnomernom priblizhenii na $\Bbb R^2$ nepreryvnykh banakhovoznachnykh funktsii”, Vestnik Sankt-Peterburgskogo universiteta. Seriya 1. Matematika. Mekhanika. Astronomiya, 2005, no. 2, 11–24 | Zbl

[4] V. S. Kalnitskii, “Pryamougolnaya triangulyatsiya mnogougolnikov”, Vestnik Sankt-Peterburgskogo universiteta. Seriya 1. Matematika. Mekhanika. Astronomiya, 3(61):4 (2016), 594–601 | MR