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In geometry, the exsphere of a face of a regular polyhedron is the sphere outside the polyhedron which touches the face and the planes defined by extending the adjacent faces outwards. It is tangent to the face externally and tangent to the adjacent faces internally. It is the 3-dimensional equivalent of the excircle. The sphere is more generally well-defined for any face which is a regular polygon and delimited by faces with the same dihedral angles at the shared edges. Faces of semi-regular polyhedra often have different types of faces, which define exspheres of different size with each type of face. == Parameters == The exsphere touches the face of the regular polyedron at the center of the incircle of that face. If the exsphere radius is denoted , the radius of this incircle and the dihedral angle between the face and the extension of the adjacent face , the center of the exsphere is located from the viewpoint at the middle of one edge of the face by bisecting the dihedral angle. Therefore : is the 180-degree complement of the internal face-to-face angle. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Exsphere (polyhedra)」の詳細全文を読む スポンサード リンク
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