Fundamental polygon (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Fundamental polygon" in English language version.

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Note that a simple polygon in the plane with n ≥ 4 vertices is homeomorphic to one, and hence any, convex n-gon by a piecewise linear homeomorphism, linear on the edges: this follows by induction on n from the observation of Max Dehn that any simple polygon possesses a diagonal, i.e. an interior chord between vertices, so can be broken up into smaller polygons; see Guggenheimer (1977). For a regular 4g-gon, the pairing between sides can be made linear, by reparametrising triangles made up of the centre and one side from each pair of sides. Guggenheimer, H. (1977), "The Jordan curve theorem and an unpublished manuscript by Max Dehn" (PDF), Archive for History of Exact Sciences, 17 (2): 193–200, CiteSeerX 10.1.1.374.1893, doi:10.1007/BF02464980, JSTOR 41133486, MR 0532231

Note that a simple polygon in the plane with n ≥ 4 vertices is homeomorphic to one, and hence any, convex n-gon by a piecewise linear homeomorphism, linear on the edges: this follows by induction on n from the observation of Max Dehn that any simple polygon possesses a diagonal, i.e. an interior chord between vertices, so can be broken up into smaller polygons; see Guggenheimer (1977). For a regular 4g-gon, the pairing between sides can be made linear, by reparametrising triangles made up of the centre and one side from each pair of sides. Guggenheimer, H. (1977), "The Jordan curve theorem and an unpublished manuscript by Max Dehn" (PDF), Archive for History of Exact Sciences, 17 (2): 193–200, CiteSeerX 10.1.1.374.1893, doi:10.1007/BF02464980, JSTOR 41133486, MR 0532231

Note that a simple polygon in the plane with n ≥ 4 vertices is homeomorphic to one, and hence any, convex n-gon by a piecewise linear homeomorphism, linear on the edges: this follows by induction on n from the observation of Max Dehn that any simple polygon possesses a diagonal, i.e. an interior chord between vertices, so can be broken up into smaller polygons; see Guggenheimer (1977). For a regular 4g-gon, the pairing between sides can be made linear, by reparametrising triangles made up of the centre and one side from each pair of sides. Guggenheimer, H. (1977), "The Jordan curve theorem and an unpublished manuscript by Max Dehn" (PDF), Archive for History of Exact Sciences, 17 (2): 193–200, CiteSeerX 10.1.1.374.1893, doi:10.1007/BF02464980, JSTOR 41133486, MR 0532231

E. Fedorov (1891) "Симметрія на плоскости" (Simmetriya na ploskosti, Symmetry in the plane), Записки Императорского С.-Петербургского минералогического общества (Zapiski Imperatorskova Sankt-Petersburgskova Mineralogicheskova Obshchestva, Proceedings of the Imperial St. Petersburg Mineralogical Society), 2nd series, 28 : 345–390 (in Russian).
E. Fedorov (1891) "Симметрія на плоскости" (Simmetriya na ploskosti, Symmetry in the plane), Записки Императорского С.-Петербургского минералогического общества (Zapiski Imperatorskova Sankt-Petersburgskova Mineralogicheskova Obshchestva, Proceedings of the Imperial St. Petersburg Mineralogical Society), 2nd series, 28 : 345–390 (in Russian).

Note that a simple polygon in the plane with n ≥ 4 vertices is homeomorphic to one, and hence any, convex n-gon by a piecewise linear homeomorphism, linear on the edges: this follows by induction on n from the observation of Max Dehn that any simple polygon possesses a diagonal, i.e. an interior chord between vertices, so can be broken up into smaller polygons; see Guggenheimer (1977). For a regular 4g-gon, the pairing between sides can be made linear, by reparametrising triangles made up of the centre and one side from each pair of sides. Guggenheimer, H. (1977), "The Jordan curve theorem and an unpublished manuscript by Max Dehn" (PDF), Archive for History of Exact Sciences, 17 (2): 193–200, CiteSeerX 10.1.1.374.1893, doi:10.1007/BF02464980, JSTOR 41133486, MR 0532231

Note that a simple polygon in the plane with n ≥ 4 vertices is homeomorphic to one, and hence any, convex n-gon by a piecewise linear homeomorphism, linear on the edges: this follows by induction on n from the observation of Max Dehn that any simple polygon possesses a diagonal, i.e. an interior chord between vertices, so can be broken up into smaller polygons; see Guggenheimer (1977). For a regular 4g-gon, the pairing between sides can be made linear, by reparametrising triangles made up of the centre and one side from each pair of sides. Guggenheimer, H. (1977), "The Jordan curve theorem and an unpublished manuscript by Max Dehn" (PDF), Archive for History of Exact Sciences, 17 (2): 193–200, CiteSeerX 10.1.1.374.1893, doi:10.1007/BF02464980, JSTOR 41133486, MR 0532231