A nonregular Tetrahedron in which each pair of opposite Edges are equal such that all triangular faces are congruent. A Tetrahedron is isosceles Iff the sum of the face angles at each Vertex is 180°, and Iff its Insphere and Circumsphere are concentric.

The only way for all the faces of a Tetrahedron to have the same Perimeter or to have the same Area is for them to be fully congruent, in which case the tetrahedron is isosceles.

**References**

Brown, B. H. ``Theorem of Bang. Isosceles Tetrahedra.'' *Amer. Math. Monthly* **33**, 224-226, 1926.

Honsberger, R. ``A Theorem of Bang and the Isosceles Tetrahedron.'' Ch. 9 in *Mathematical Gems II.*
Washington, DC: Math. Assoc. Amer., pp. 90-97, 1976.

© 1996-9

1999-05-26