5, and additional sets of cubic space group orbifolds are illustrated. The overall structure of the cubic space group families is summarized in Sect. Appendix A discusses the color crystallographic groups, which have both symmetry and antisymmetry elements. The graphic color elliptic 2-orbifold symbols shown in Appendix B may be used in the construction of orbifold covers. We have basic results covering most of the space groups but have not found an optimal format for their presentation.
Critical points occur where the first derivative of the global density is zero.
A degenerate critical point will have a singular second derivative matrix with one or more zero or nearly zero eigenvalues. 1.1 and 1.2, are topologically unique. Additional examples are given in Sect. In experimentally derived crystallographic macromolecule electron-density functions, this will not be the case because of critical point merging caused by inadequate resolution experimental data. Critical Net for NaCl Fig.