Florestan Brunck (McGill University)

Title: Non-Obtuse Dissection of Tetrahedra.

In the plane any obtuse triangle can be dissected into 2 right-angled triangles by drawing the altitude from the obtuse vertex on its opposite side. The problem generalises naturally to higher dimensions, where we consider a simplex to be non-obtuse provided no angle between two co-dimension 1 faces is obtuse. The problem at hand is then stated in an open conjecture due to Hadwiger (1956): can every d-simplex be dissected into non-obtuse d-simplices? We provide a constructive answer to this interesting puzzle in dimension 3, where we show that

28 orthoschemes are sufficient to dissect any tetrahedron.