. 2020 Nov 17;11:5862. doi: 10.1038/s41467-020-19752-3

Table 1.

The number of equivalent but different orientations of a 2D material on a substrate based on the interplay between their symmetries.

G_2D	C_6V				C_4V				C_3V				C_2V
G_Sub	C_6V	C_4V	C_3V	C_2V	C_6V	C_4V	C_3V	C_2V	C_6V	C_4V	C_3V	C_2V	C_6V	C_4V	C_3V	C_2V
G_2D@Sub	C_6V	C_2V	C_3V	C_2V	C_2V	C_4V	C_V	C_2V	C_3V	C_V	C_3V	C_V	C_2V	C_2V	C_V	C_2V
∣G_sub∣	12	8	6	4	12	8	6	4	12	8	6	4	12	8	6	4
∣G_2D@sub∣	12	4	6	4	4	8	2	4	6	2	6	2	4	4	2	4
N₁	1	2	1	1	3	1	3	1	2	4	1	2	3	2	3	1

Here, G_Sub, G_2D and G_2D@Sub are symmetry groups of the substrate, the 2D material and the 2D material–substrate system, ∣G_sub∣ and ∣G_2D@sub∣ are the orders of G_Sub and G_2D@Sub; and N₁ = ∣G_sub∣/∣G_2D@sub∣ is the number of equivalent but different directions of the 2D material on the substrate.