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- Inscribed_sphere abstract "In geometry, the inscribed sphere or insphere of a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces. It is the largest sphere that is contained wholly within the polyhedron, and is dual to the dual polyhedron's circumsphere.All regular polyhedra have inscribed spheres, but most irregular polyhedra do not have all facets tangent to a common sphere, although it is still possible to define the largest contained sphere for such shapes. For such cases, the notion of an insphere does not seem to have been properly defined and various interpretations of an insphere are to be found: The sphere tangent to all faces (if one exists). The sphere tangent to all face planes (if one exists). The sphere tangent to a given set of faces (if one exists). The largest sphere that can fit inside the polyhedron.Often these spheres coincide, leading to confusion as to exactly what properties define the insphere for polyhedra where they do not coincide.For example the regular small stellated dodecahedron has a sphere tangent to all faces, while a larger sphere can still be fitted inside the polyhedron. Which is the insphere? Important authorities such as Coxeter or Cundy & Rollett are clear enough that the face-tangent sphere is the insphere. Again, such authorities agree that the Archimedean polyhedra (having regular faces and equivalent vertices) have no inspheres while the Archimedean dual or Catalan polyhedra do have inspheres. But many authors fail to respect such distinctions and assume other definitions for the 'inspheres' of their polyhedra.The radius of the sphere inscribed in a polyhedron P is called the inradius of P.".
- Inscribed_sphere wikiPageID "991786".
- Inscribed_sphere wikiPageLength "2277".
- Inscribed_sphere wikiPageOutDegree "17".
- Inscribed_sphere wikiPageRevisionID "587184151".
- Inscribed_sphere wikiPageWikiLink Archimedean_solid.
- Inscribed_sphere wikiPageWikiLink Catalan_solid.
- Inscribed_sphere wikiPageWikiLink Category:Elementary_geometry.
- Inscribed_sphere wikiPageWikiLink Category:Polyhedra.
- Inscribed_sphere wikiPageWikiLink Category:Spheres.
- Inscribed_sphere wikiPageWikiLink Circumscribed_sphere.
- Inscribed_sphere wikiPageWikiLink Convex_polytope.
- Inscribed_sphere wikiPageWikiLink Dual_polyhedron.
- Inscribed_sphere wikiPageWikiLink Duality_(mathematics).
- Inscribed_sphere wikiPageWikiLink Geometry.
- Inscribed_sphere wikiPageWikiLink Incircle_and_excircles_of_a_triangle.
- Inscribed_sphere wikiPageWikiLink Midsphere.
- Inscribed_sphere wikiPageWikiLink Regular_polyhedron.
- Inscribed_sphere wikiPageWikiLink Small_stellated_dodecahedron.
- Inscribed_sphere wikiPageWikiLink Sphere.
- Inscribed_sphere wikiPageWikiLink Tangent.
- Inscribed_sphere wikiPageWikiLinkText "Inscribed sphere".
- Inscribed_sphere wikiPageWikiLinkText "Insphere".
- Inscribed_sphere wikiPageWikiLinkText "inscribed sphere".
- Inscribed_sphere wikiPageWikiLinkText "inscribed".
- Inscribed_sphere wikiPageWikiLinkText "insphere".
- Inscribed_sphere title "Insphere".
- Inscribed_sphere urlname "Insphere".
- Inscribed_sphere wikiPageUsesTemplate Template:Elementary-geometry-stub.
- Inscribed_sphere wikiPageUsesTemplate Template:Mathworld.
- Inscribed_sphere subject Category:Elementary_geometry.
- Inscribed_sphere subject Category:Polyhedra.
- Inscribed_sphere subject Category:Spheres.
- Inscribed_sphere hypernym Sphere.
- Inscribed_sphere type ArtificialSatellite.
- Inscribed_sphere type Polytope.
- Inscribed_sphere type Redirect.
- Inscribed_sphere comment "In geometry, the inscribed sphere or insphere of a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.".
- Inscribed_sphere label "Inscribed sphere".
- Inscribed_sphere sameAs Q683362.
- Inscribed_sphere sameAs كرة_داخلية.
- Inscribed_sphere sameAs Inkugel.
- Inscribed_sphere sameAs Enskribita_sfero.
- Inscribed_sphere sameAs Esfera_inscrita.
- Inscribed_sphere sameAs Kula_wpisana.
- Inscribed_sphere sameAs m.03xbck.
- Inscribed_sphere sameAs Q683362.
- Inscribed_sphere sameAs 内切球.
- Inscribed_sphere wasDerivedFrom Inscribed_sphere?oldid=587184151.
- Inscribed_sphere isPrimaryTopicOf Inscribed_sphere.