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Regular polyhedron
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===Interior points=== The sum of the distances from any point in the interior of a regular polyhedron to the sides is independent of the location of the point (this is an extension of [[Viviani's theorem]].) However, the converse does not hold, not even for [[tetrahedra]].<ref>Chen, Zhibo, and Liang, Tian. "The converse of Viviani's theorem", ''[[The College Mathematics Journal]]'' 37(5), 2006, pp. 390β391.</ref>
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