Table 1 Classifications C of TCIs for noninteracting electrons with time-reversal symmetry, spin-orbit coupling, and crystalline point group symmetry.

N/A denotes a trivial classification. Full classifications including strong topological insulators can be easily obtained from this table by using the group extension rules given in Results and are also provided as a table in the Supplementary Materials.

Point groupTCI classification
1N/A
1¯2
22
m
2/mℤ × ℤ2
22222
mm22
mmm3
42
4¯2
4/mℤ × ℤ2
42222
4mm2
4¯2mℤ × ℤ2
4/mmm3
3N/A
3¯2
322
3m
3¯mℤ × ℤ2
62
6¯
6/mℤ × ℤ2
62222
6mm2
6¯2m2
6/mmm3
23N/A
m3¯
4322
4¯3m
m3¯m2