Incugel

Inball (red) of a cube

The inc sphere of a polyhedron is a sphere that touches all faces of the given polyhedron. In addition to the edge sphere , the incircle is in spatial geometry what the inscribed circle of a polygon is in plane geometry .

The center of an inc sphere must have the same distance from all boundary surfaces. It must therefore be located on all planes of symmetry (planes bisecting the angle) to two limiting planes each. Since the intersection of these planes is generally empty, only special polyhedra have an incphere, in particular all tetrahedra (not only the regular ones!) And the five Platonic solids . All Catalan solids also have an inc sphere, since their respective boundary surfaces are all the same ( congruent ) with one another .

See also

• Edge ball
• Umkugel
• Inscribed circle

Web links

Wiktionary: Inkugel  - explanations of meanings, word origins, synonyms, translations

• Eric W. Weisstein : Insphere . In: MathWorld (English).
• Venn diagram for the description of spheres around , in and edge of polyhedra