Supplemental Data and Programs for
Dihedral Acute Triangulation of the Cube

There is a dihedral acute triangulation of the cube, and because there is one, there are, in fact, infinitely many combinatorially different acute triangulations of the cube. In 2009, E. VanderZee, A. Hirani, V. Zharnitsky, and D. Guoy discovered an acute triangulation of the cube with 1370 tetrahedra (Details are in the preprint here). The vertices of that acute triangulation are available here. The triangulation is the Delaunay triangulation of the set of vertices.

MATLAB has a function that computes the 3-dimensional Delaunay triangulation of a set of points, so it's possible to write a fairly short MATLAB script that computes the triangulation from the set of vertices and verifies that the triangulation is, indeed, dihedral acute. We provide such a script here. The script is not robust in terms of error checking, but given a file with a list of points in 3-dimensional Euclidean space, it reads the points from the file, computes their Delaunay triangulation, and computes the dihedral angles and face angles of the tetrahedra of the Delaunay triangulation.

To cite this webpage, the vertex data, or the program linked from this page, please use this.


Page maintained by Evan VanderZee and Anil N. Hirani. Last updated May 29, 2009.