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46:, and segments are drawn from the points of tangency to each vertex on the same face of the tetrahedron, then all four points of tangency have the same triple of angles. In particular, it follows that the 12 triangles into which the segments subdivide the faces of the tetrahedron form congruent pairs across each edge of the tetrahedron. It is named after A. S. Bang, who posed it as a problem in 1897.
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Brown, B. H. (April 1926), "Theorem of Bang. Isosceles tetrahedra", Undergraduate
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On angles formed when a sphere is inscribed within a tetrahedron
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100:"Opgaver til Løsning",
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