Section 2.1.7.4. Graphs for plane groups

There are no graphs for plane groups in this volume. The four graphs for t-subgroups of plane groups are apart from the symbols the same as those for the corresponding space groups: –, –, – and –, where the graphs for the space groups are included in the t-subgroup graphs in Figs. 2.4.1.1 , 2.4.3.1 , 2.4.2.1 and 2.4.2.3 , respectively.

The k-subgroup graphs are trivial for the plane groups , , , , and because there is only one plane group in its crystal class. The graphs for the crystal classes and consist of two plane groups each: and , and . Nevertheless, the graphs are different: the relation is one-sided for the tetragonal plane-group pair as it is in the space-group pair and it is two-sided for the hexagonal plane-group pair as it is in the space-group pair (81)– (82). The graph for the three plane groups of the crystal class m corresponds to the space-group graph for the crystal class 2.

Finally, the graph for the four plane groups of crystal class has no direct analogue among the k-subgroup graphs of the space groups. It can be obtained, however, from the graph in Fig. 2.5.1.3 of crystal class by removing the fields of (15) and (11) with all their connections to the remaining fields. The replacements are then: (12) by (9), (10) by (6), (13) by (7) and (14) by (8).