About: Exsphere (polyhedra)

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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.

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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 regularpolygon and delimited by faces with the same dihedral anglesat 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. (en)
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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. (en)
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  • Exsphere (polyhedra) (en)
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