Two characterizations of the Hill-tetrahedra (Q5954168)

In 1896 M. J. M. Hill researched some special tetrahedrons in the 3-dimensional Euclidean space which were called Hill tetrahedrons. The underlying paper presents two different characterizations of the Hill tetrahedrons. The main results are: A tetrahedron \(S\) allows a canonical simplex decomposition with \(H\)-congruent prisms if and only if \(S\) is a Hill tetrahedron (Satz 2). The three tetrahedrons of the canonical prism decomposition are pairwise congruent iff one of them is a Hill tetrahedron (Satz 3).