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- Szilassi_polyhedron abstract "The Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces.Each face of this polyhedron shares an edge with each other face. As a result, it requires seven colours to colour each adjacent face, providing the lower bound for the seven colour theorem. It has an axis of 180-degree symmetry; three pairs of faces are congruent leaving one unpaired hexagon that has the same rotational symmetry as the polyhedron. The 14 vertices and 21 edges of the Szilassi polyhedron form an embedding of the Heawood graph onto the surface of a torus.The tetrahedron and the Szilassi polyhedron are the only two known polyhedra in which each face shares an edge with each other face. If a polyhedron with f faces is embedded onto a surface with h holes, in such a way that each face shares an edge with each other face, it follows by some manipulation of the Euler characteristic thatThis equation is satisfied for the tetrahedron with h = 0 and f = 4, and for the Szilassi polyhedron with h = 1 and f = 7. The next possible solution, h = 6 and f = 12, would correspond to a polyhedron with 44 vertices and 66 edges, but it is not known whether such a polyhedron exists. More generally this equation can be satisfied precisely when f is congruent to 0, 3, 4, or 7 modulo 12.The Szilassi polyhedron is named after Hungarian mathematician Lajos Szilassi, who discovered it in 1977. The dual to the Szilassi polyhedron, the Császár polyhedron, was discovered earlier by Ákos Császár (1949); it has seven vertices, 21 edges connecting every pair of vertices, and 14 triangular faces. Like the Szilassi polyhedron, the Császár polyhedron has the topology of a torus.".
- Szilassi_polyhedron thumbnail Szilassi_polyhedron.svg?width=300.
- Szilassi_polyhedron wikiPageExternalLink cutoutfoldup.com.
- Szilassi_polyhedron wikiPageExternalLink 0927_a4.pdf.
- Szilassi_polyhedron wikiPageExternalLink st13-06-a3-ocr.pdf.
- Szilassi_polyhedron wikiPageExternalLink mathtrek_01_22_07.html.
- Szilassi_polyhedron wikiPageExternalLink szilassi.html.
- Szilassi_polyhedron wikiPageID "7652409".
- Szilassi_polyhedron wikiPageRevisionID "581367694".
- Szilassi_polyhedron authorlink "Ákos Császár".
- Szilassi_polyhedron dual Császár_polyhedron.
- Szilassi_polyhedron edges "21".
- Szilassi_polyhedron euler "0".
- Szilassi_polyhedron faces "7".
- Szilassi_polyhedron first "Ákos".
- Szilassi_polyhedron hasPhotoCollection Szilassi_polyhedron.
- Szilassi_polyhedron last "Császár".
- Szilassi_polyhedron properties "Nonconvex".
- Szilassi_polyhedron symmetry "C1, [ ]+,".
- Szilassi_polyhedron title "Szilassi Polyhedron".
- Szilassi_polyhedron type Toroidal_polyhedron.
- Szilassi_polyhedron urlname "SzilassiPolyhedron".
- Szilassi_polyhedron vertexConfig "6.6".
- Szilassi_polyhedron vertices "14".
- Szilassi_polyhedron year "1949".
- Szilassi_polyhedron subject Category:Nonconvex_polyhedra.
- Szilassi_polyhedron subject Category:Toroidal_polyhedra.
- Szilassi_polyhedron comment "The Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces.Each face of this polyhedron shares an edge with each other face. As a result, it requires seven colours to colour each adjacent face, providing the lower bound for the seven colour theorem. It has an axis of 180-degree symmetry; three pairs of faces are congruent leaving one unpaired hexagon that has the same rotational symmetry as the polyhedron.".
- Szilassi_polyhedron label "Poliedro de Szilassi".
- Szilassi_polyhedron label "Poliedro di Szilassi".
- Szilassi_polyhedron label "Polyèdre de Szilassi".
- Szilassi_polyhedron label "Szilassi polyhedron".
- Szilassi_polyhedron label "Szilassi-Polyeder".
- Szilassi_polyhedron label "Szilassi多面體".
- Szilassi_polyhedron sameAs Szilassi-Polyeder.
- Szilassi_polyhedron sameAs Poliedro_de_Szilassi.
- Szilassi_polyhedron sameAs Szilassiren_poliedro.
- Szilassi_polyhedron sameAs Polyèdre_de_Szilassi.
- Szilassi_polyhedron sameAs Poliedro_di_Szilassi.
- Szilassi_polyhedron sameAs m.0267x_m.
- Szilassi_polyhedron sameAs Q838442.
- Szilassi_polyhedron sameAs Q838442.
- Szilassi_polyhedron wasDerivedFrom Szilassi_polyhedron?oldid=581367694.
- Szilassi_polyhedron depiction Szilassi_polyhedron.svg.
- Szilassi_polyhedron isPrimaryTopicOf Szilassi_polyhedron.