Geodesic
A Note on Bang's Theorem on Equifacial Tetrahedra
Journal for geometry and graphics, Tome 8 (2004) no. 2, pp. 163-169.

Voir la notice de l'article provenant de la source Heldermann Verlag

We give an analytic proof based on Pythagoras' theorem of a theorem of Bang stating that if the faces of a tetrahedron have equal areas then they are congruent. We also place Bang's theorem in the more general context that deals with the existence and uniqueness of a tetrahedron PABC having a given base ABC and having lateral faces of given areas. Our approach shows also how to construct counter-examples to Bang's statement in higher dimensions.
Classification : 51M20, 52B11
Mots-clés : Isosceles tetrahedron, equifacial tetrahedron, Bang's Theorem, regular simplex, barycentric coordinates, trilinear coordinates 
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     title = {A {Note} on {Bang's} {Theorem} on {Equifacial} {Tetrahedra}},
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M. Hajja; F. Saidi . A Note on Bang's Theorem on Equifacial Tetrahedra. Journal for geometry and graphics, Tome 8 (2004) no. 2, pp. 163-169. http://geodesic.mathdoc.fr/item/JGG_2004_8_2_JGG_2004_8_2_a3/