Geometry of Delaunay simplices

We investigated differences between classes of simplices using geometrical parameters of tetrahedra such as volume and tetrahedrality. Tetrahedrality is a quantitative measure of the degree of distortion of the Delaunay simplices from the ideal tetrahedron:

where is the length of the i-th edge, and is the mean length of the edges of the given simplex. Distributions of volume and tetrahedrality for all five classes of simplices is shown in Figure 3. The sharpest peaks correspond to the simplices of classes {4} and {2,2}. They tend to have the lowest volume and lowest distortion of tetrahedrality. These results suggest that tetrahedra of these two classes may occur in regular protein conformations such as a-helices.