Geodesic
Equifaciality of Tetrahedra whose Incenter and Fermat-Torricelli Center Coincide
Journal for geometry and graphics, Tome 9 (2005) no. 1, pp. 37-41 Cet article a éte moissonné depuis la source Heldermann Verlag

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We show that if the incenter and the Fermat-Torricelli center of a tetrahedron coincide, then the tetrahedron is equifacial (or isosceles) in the sense that all its faces are congruent. The proof is intended to replace the incorrect proof given in a previous paper of the authors [Internat. J. Math. Ed. Sci. Tech. 32 (2001) 501--508] for the same statement.
Classification : 51M04, 51M20, 52B10
Mots-clés : Barycentric coordinates, Fermat-Torricelli center, isosceles tetrahedron, equifacial tetrahedron 
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     title = {Equifaciality of {Tetrahedra} whose {Incenter} and {Fermat-Torricelli} {Center} {Coincide}},
     journal = {Journal for geometry and graphics},
     pages = {37--41},
     year = {2005},
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M. Hajja; P. Walker . Equifaciality of Tetrahedra whose Incenter and Fermat-Torricelli Center Coincide. Journal for geometry and graphics, Tome 9 (2005) no. 1, pp. 37-41. http://geodesic.mathdoc.fr/item/JGG_2005_9_1_JGG_2005_9_1_a3/