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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 wikiPageRevisionID "587184151".
- Inscribed_sphere hasPhotoCollection Inscribed_sphere.
- Inscribed_sphere title "Insphere".
- Inscribed_sphere urlname "Insphere".
- Inscribed_sphere subject Category:Elementary_geometry.
- Inscribed_sphere subject Category:Polyhedra.
- Inscribed_sphere subject Category:Spheres.
- Inscribed_sphere type Abstraction100002137.
- Inscribed_sphere type Attribute100024264.
- Inscribed_sphere type Environment113934596.
- Inscribed_sphere type Situation113927383.
- Inscribed_sphere type Sphere114514039.
- Inscribed_sphere type Spheres.
- Inscribed_sphere type State100024720.
- 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 "Inkugel".
- Inscribed_sphere label "Inscribed sphere".
- Inscribed_sphere label "Kula wpisana".
- Inscribed_sphere label "كرة داخلية".
- Inscribed_sphere label "内切球".
- Inscribed_sphere sameAs Inkugel.
- Inscribed_sphere sameAs Kula_wpisana.
- Inscribed_sphere sameAs m.03xbck.
- Inscribed_sphere sameAs Q683362.
- Inscribed_sphere sameAs Q683362.
- Inscribed_sphere sameAs Inscribed_sphere.
- Inscribed_sphere wasDerivedFrom Inscribed_sphere?oldid=587184151.
- Inscribed_sphere isPrimaryTopicOf Inscribed_sphere.