Only some of the pales are required by symmetry to be exactly in the plane of the chemical faces. Critical Net Illustration of Face-Centered Cubic. Critical Net Characteristics Below are some definitive characteristics that are useful for finding and analyzing critical nets for very simple structures. High precision experimental electron density maps from x-ray data and charge density maps calculated by ab initio quantum chemistry programs are more complicated than those considered here because of the possible addition of new critical points caused by bonding electrons etc. Peaks are at atom positions.
Pits are as far from all adjacent peaks as possible.
A pass lies between two adjacent peaks. A pale lies between two adjacent pits. Wyckoff position of the space group must contain a critical point of the crystal structure. To satisfy the first two Morse inequalities above, the Morse inequalities are applied to the basic unit or the unit cell rather than the asymmetric unit so that we are always working with integers rather than rational numbers. This count is identical to that for the four topology Betti numbers of a 3-torus.