  All of 320 layer groups, distributed into 80 clusters - single/double
ordinary/gray groups - are used to complete systematization of linear (in all
directions) band crossings and corresponding effective Hamiltonians in
high-symmetry Brillouin zone points of layered materials, refining and
expanding in literature existing data. Two- and four-dimensional effective
Hamiltonians are determined by the allowed (half)integer (co)representations of
the same dimension in the crossing point and one- or two-dimensional generic
allowed representations. The resulting dispersion types (having isotropic or
anisotropic form) are: single cone (with double degenerate crossing point and
non-degenerate branches, or 4-fold degenerate crossing point with double
degenerate conical branches), poppy-flower (4-fold degenerate crossing point
with two pairs of non-degenerate mutually rotated conical branches), and a
fortune teller (with nodal lines). Transition to double group, enabling to
include spin-orbit interaction, results in various scenarios at high symmetry
points: gap closing, gap opening, cone preserving, cone splitting etc.
Analogously, analyzing ordinary to gray group transitions, the role of time
reversal symmetry is clarified.
