(1) Arithmetic crystal class . The parameter ranges for the special lines and planes of the asymmetric unit and for general k vectors of the reciprocalspace group [setting ] are listed in Tables 1.5.5.3 and 1.5.5.4. One can describe the corresponding conditions of the representation domain by the boundary plane = which for forms the triangle [] in Fig. 1.5.5.3 but for the pentagon [] in Fig. 1.5.5.4. The inner points of this boundary plane are points of the general position GP with the exception of the line , which is a twofold rotation axis. The boundary conditions for the representation domain depend on ; they are much more complicated than those, , for the asymmetric unit.
(2) Arithmetic crystal class , see Figs. 1.5.5.5 to 1.5.5.7. In the reciprocalspace group the lines and LE belong to Wintgen position , as do the lines and if present. The lines and belong to the Wintgen position ; as do the lines and if present. The lines , , A, A_{1}, C and U belong to the plane ; the lines , B, B_{1} and D belong to the plane . The decisive boundary plane of the representation domain is , where ; it is a hexagon for Fig. 1.5.5.5 and a parallelogram for Figs. 1.5.5.6 and 1.5.5.7. There is no relation of the lattice parameters for which all the abovementioned lines are realized on the surface of the representation domain simultaneously; either two or three of them do not appear and the length of the others depends on the boundary plane, see Tables and Figs. 1.5.5.5 to 1.5.5.7.
The boundary conditions for the asymmetric unit are independent of the lattice parameters and the boundary plane is always represented by the simple equation : . By introducing flagpoles and wings, the description may become uniarm.
