# Acute-dihedral triangulation of the cube

VanderZee et al have solved an open problem in mesh generation from one of my earlier papers (with Sullivan and Üngör): is there a partition of a cube into tetrahedra, meeting triangle-to-triangle and edge-to-edge, with the property that ell the dihedral angles of every tetrahedron are acute? In our earlier work, we were only able to show the existence of acute triangulations of this type for infinite slabs, but the new paper shows that they do exist for cubes. The triangulation they find is well-behaved in other ways as well: the angles are bounded well away from right angles, and every tetrahedron contains its circumcenter.

This work raises the possibility that every polyhedron has an acute triangulation, but that remains an open problem still.