
Journal for Geometry and Graphics 09 (2005), No. 1, 037041 Copyright Heldermann Verlag 2005 Equifaciality of Tetrahedra whose Incenter and FermatTorricelli Center Coincide Mowaffaq Hajja Dept. of Mathematics, Yarmouk University, Irbid, Jordan mhajja@yu.edu.jo Peter Walker Dept. of Mathematics and Statistics, American University, P. O. Box 26666, Sharjah, United Arab Emirates peterw@aus.ac.ae We show that if the incenter and the FermatTorricelli 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) 501508] for the same statement. Keywords: Barycentric coordinates, FermatTorricelli center, isosceles tetrahedron, equifacial tetrahedron. MSC: 51M04; 51M20, 52B10 [ Fulltextpdf (90 KB)] for subscribers only. 