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circumscribed sphere
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.〔.〕 As in the case of two-dimensional circumscribed circles, the radius of a sphere circumscribed around a polyhedron ''P'' is called the circumradius of ''P'',〔.〕 and the center point of this sphere is called the circumcenter of ''P''.〔.〕
==Existence and optimality==
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. However, the smallest sphere containing a given polyhedron is always the circumsphere of the convex hull of a subset of the vertices of the polyhedron.〔.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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