
Journal for Geometry and Graphics 23 (2019), No. 1, 037040 Copyright Heldermann Verlag 2019 Characterization of an Isosceles Tetrahedron Hidefumi Katsuura Dept. of Mathematics, San Jose State University, One Washington Square, San Jose, CA 95192, U.S.A. hidefumi.katsuura@sjsu.edu A tetrahedron in which each edge is equal to its opposite is an {isosceles} tetrahedron. We will use vectors to prove the following statement: A tetrahedron OABC is isosceles if, and only if the centroid of the parallelepiped defined by the three edges OA, OB, and OC is an excenter of the tetrahedron OABC. Keywords: Isosceles tetrahedron, incenter, excenter, centroid, circumcenter. MSC: 52B10; 51M04, 51N20 [ Fulltextpdf (183 KB)] 