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midsphere
In geometry, the midsphere or intersphere of a polyhedron is a sphere which is tangent to every ''edge'' of the polyhedron. That is to say, it touches any given edge at exactly one point. Not every polyhedron has a midsphere, but for every polyhedron there is a combinatorially equivalent polyhedron, the canonical polyhedron, that does have a midsphere.
The midsphere is so-called because, for polyhedra that have a midsphere, an inscribed sphere (which is tangent to every face of a polyhedron) and a circumscribed sphere (which touches every vertex), the midsphere is in the middle, between the other two spheres. The radius of the midsphere is called the midradius.
==Examples==
The uniform polyhedra, including the regular, quasiregular and semiregular polyhedra and their duals all have midspheres. In the regular polyhedra, the inscribed sphere, midsphere, and circumscribed sphere all exist and are concentric.〔 states this for regular polyhedra; for archimedean polyhedra.〕
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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