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- Toroidal_polyhedron abstract "In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus of 1 or greater.Non-self-intersecting toroidal polyhedra are embedded toroids, while self-intersecting toroidal polyhedra are toroidal as abstract polyhedra, which can be verified by their Euler characteristic (0 or less), and their self-intersecting realization in Euclidean 3-space is a polyhedral immersion.If a toroidal polyhedron is non-orientable then it cannot be embedded in 3-space, for example the Klein bottle is a non-orientable toroid of Euler characteristic 0. If the toroid has an odd-valued Euler characteristic then it cannot be embedded, however the Klein bottle demonstrates that the converse is not true.".
- Toroidal_polyhedron thumbnail Excavated_expanded_cuboctahedron.png?width=300.
- Toroidal_polyhedron wikiPageExternalLink ToroidalPolyhedra.html.
- Toroidal_polyhedron wikiPageExternalLink Stewart_.htm.
- Toroidal_polyhedron wikiPageExternalLink 0686119363.
- Toroidal_polyhedron wikiPageExternalLink Stewart.
- Toroidal_polyhedron wikiPageExternalLink stewart.htm.
- Toroidal_polyhedron wikiPageID "24804975".
- Toroidal_polyhedron wikiPageLength "5143".
- Toroidal_polyhedron wikiPageOutDegree "47".
- Toroidal_polyhedron wikiPageRevisionID "668848831".
- Toroidal_polyhedron wikiPageWikiLink Abstract_polyhedra.
- Toroidal_polyhedron wikiPageWikiLink Abstract_polytope.
- Toroidal_polyhedron wikiPageWikiLink Bonnie_Stewart.
- Toroidal_polyhedron wikiPageWikiLink Category:Toroidal_polyhedra.
- Toroidal_polyhedron wikiPageWikiLink Convex_hull.
- Toroidal_polyhedron wikiPageWikiLink Császár_polyhedron.
- Toroidal_polyhedron wikiPageWikiLink Deltahedron.
- Toroidal_polyhedron wikiPageWikiLink Dual_polyhedron.
- Toroidal_polyhedron wikiPageWikiLink Embedding.
- Toroidal_polyhedron wikiPageWikiLink Euler_characteristic.
- Toroidal_polyhedron wikiPageWikiLink Genus_(mathematics).
- Toroidal_polyhedron wikiPageWikiLink Geometry.
- Toroidal_polyhedron wikiPageWikiLink Great_dodecahedron.
- Toroidal_polyhedron wikiPageWikiLink Hexagonal_prism.
- Toroidal_polyhedron wikiPageWikiLink Immersion_(mathematics).
- Toroidal_polyhedron wikiPageWikiLink Infinite_skew_polyhedron.
- Toroidal_polyhedron wikiPageWikiLink Isogonal_figure.
- Toroidal_polyhedron wikiPageWikiLink Isohedral_figure.
- Toroidal_polyhedron wikiPageWikiLink Johnson_solid.
- Toroidal_polyhedron wikiPageWikiLink Klein_bottle.
- Toroidal_polyhedron wikiPageWikiLink Noble_polyhedron.
- Toroidal_polyhedron wikiPageWikiLink Octahedra.
- Toroidal_polyhedron wikiPageWikiLink Octahedron.
- Toroidal_polyhedron wikiPageWikiLink Octahemioctahedron.
- Toroidal_polyhedron wikiPageWikiLink Polyhedron.
- Toroidal_polyhedron wikiPageWikiLink Projective_polyhedron.
- Toroidal_polyhedron wikiPageWikiLink Regular_polygon.
- Toroidal_polyhedron wikiPageWikiLink Self-dual_polyhedron.
- Toroidal_polyhedron wikiPageWikiLink Skew_apeirohedron.
- Toroidal_polyhedron wikiPageWikiLink Small_cubicuboctahedron.
- Toroidal_polyhedron wikiPageWikiLink Spherical_polyhedron.
- Toroidal_polyhedron wikiPageWikiLink Square_cupola.
- Toroidal_polyhedron wikiPageWikiLink Szilassi_polyhedron.
- Toroidal_polyhedron wikiPageWikiLink Tetrahedra.
- Toroidal_polyhedron wikiPageWikiLink Tetrahedron.
- Toroidal_polyhedron wikiPageWikiLink Toroid.
- Toroidal_polyhedron wikiPageWikiLink Torus.
- Toroidal_polyhedron wikiPageWikiLink File:Excavated_expanded_cuboctahedron.png.
- Toroidal_polyhedron wikiPageWikiLink File:Excavated_truncated_cube.png.
- Toroidal_polyhedron wikiPageWikiLink File:Great_dodecahedron.png.
- Toroidal_polyhedron wikiPageWikiLink File:Hexagonal_torus.png.
- Toroidal_polyhedron wikiPageWikiLink File:Octahemioctahedron.png.
- Toroidal_polyhedron wikiPageWikiLink File:Small_cubicuboctahedron.png.
- Toroidal_polyhedron wikiPageWikiLink File:Stephanoid5.png.
- Toroidal_polyhedron wikiPageWikiLink File:Stewart_toroid_6-hexprisms.png.
- Toroidal_polyhedron wikiPageWikiLink File:Toroidal_polyhedron.gif.
- Toroidal_polyhedron wikiPageWikiLinkText "Crown polyhedra".
- Toroidal_polyhedron wikiPageWikiLinkText "Toroidal polyhedron".
- Toroidal_polyhedron wikiPageWikiLinkText "Toroidal polyhedron#Crown polyhedra".
- Toroidal_polyhedron wikiPageWikiLinkText "Toroidal_polyhedron#Crown_polyhedra".
- Toroidal_polyhedron wikiPageWikiLinkText "Toroidal_polyhedron#Stewart_toroids".
- Toroidal_polyhedron wikiPageWikiLinkText "toroidal deltahedron".
- Toroidal_polyhedron wikiPageWikiLinkText "toroidal polyhedra".
- Toroidal_polyhedron wikiPageWikiLinkText "toroidal polyhedron".
- Toroidal_polyhedron hasPhotoCollection Toroidal_polyhedron.
- Toroidal_polyhedron title "Toroidal polyhedron".
- Toroidal_polyhedron urlname "ToroidalPolyhedron".
- Toroidal_polyhedron wikiPageUsesTemplate Template:Mathworld.
- Toroidal_polyhedron wikiPageUsesTemplate Template:Reflist.
- Toroidal_polyhedron subject Category:Toroidal_polyhedra.
- Toroidal_polyhedron hypernym Polyhedron.
- Toroidal_polyhedron type Concept.
- Toroidal_polyhedron comment "In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus of 1 or greater.Non-self-intersecting toroidal polyhedra are embedded toroids, while self-intersecting toroidal polyhedra are toroidal as abstract polyhedra, which can be verified by their Euler characteristic (0 or less), and their self-intersecting realization in Euclidean 3-space is a polyhedral immersion.If a toroidal polyhedron is non-orientable then it cannot be embedded in 3-space, for example the Klein bottle is a non-orientable toroid of Euler characteristic 0. ".
- Toroidal_polyhedron label "Toroidal polyhedron".
- Toroidal_polyhedron sameAs m.0808gpf.
- Toroidal_polyhedron sameAs Q16000355.
- Toroidal_polyhedron sameAs Q16000355.
- Toroidal_polyhedron wasDerivedFrom Toroidal_polyhedron?oldid=668848831.
- Toroidal_polyhedron depiction Excavated_expanded_cuboctahedron.png.
- Toroidal_polyhedron isPrimaryTopicOf Toroidal_polyhedron.