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Journal for Geometry and Graphics 23 (2019), No. 1, 037--040
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.

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 ex-center of the tetrahedron OABC.

Keywords: Isosceles tetrahedron, in-center, ex-center, centroid, circum-center.

MSC: 52B10; 51M04, 51N20

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