In geometry, a circumscribed sphere of a polyhedron is a sphere that contains the polyhedron and touches each of the polyhedron's vertices. The word circumsphere is sometimes used to mean the same thing. When it exists, a circumscribed sphere need not be the smallest sphere containing the polyhedron; for instance, the tetrahedron formed by a vertex of a cube and its three neighbors has the same circumsphere as the cube itself, but can be contained within a smaller sphere having the three neighboring vertices on its equator. All regular polyhedra have circumscribed spheres, but some irregular polyhedra do not have all vertices lieing on a common sphere, although it is still possible to define the smallest containing sphere for such shapes. Table of Geometry, from the 1728 Cyclopaedia. ... A polyhedron is a geometric shape which in mathematics is defined by three related meanings. ... A sphere (< Greek σφαίÏα) is a perfectly symmetrical geometrical object. ... A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. ... This article is about the geometric shape. ...
The radius of sphere circumscribed around a polyhedron P is called the circumradius of P.
Circumscribed circle In geometry, the circumscribed circle or circumcircle of a polygon is a circle which contains all the vertices of the polygon. ... A sphere containing on its surface one point from each edge of a semiregular or regular polyhedron. ... An inscribed sphere is a sphere that is enclosed by another solid object, such as a polyhedron. ...
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