The paper presents a new triangulation of ℝn, which is called the D1-triangulation, for computing zero points or fixed points of nonlinear mappings. The D1-triangulation subdivides the unit cube and is based on very elementary pivot rules. The paper compares the D1-triangulation to several well-known triangulations of ℝn which triangulate the unit cube. According to several measures of efficiency the new triangulation is superior, such as the number of simplices in the unit cube, the diameter of a triangulation, the average directional density, and the surface density.
