Table 1 Characterization of BSs in a MSG (excerpt from tables S1 to S6).

MSG*		d^†	X_BS^‡	ν_BS^§
2.4	I	9	(2, 2, 2, 4)	1
2.7	IV	5	(2)	2
3.4	IV	3	(2)	2
209.51	IV	3	(1)	2^a

*MSG number in the BNS notation, followed by a Roman numeral I, …, IV indicating its type.

†Number of linearly independent BSs.

‡Symmetry-based indicator of band topology, which takes the form , denoted by the collection of positive integers (n₁, n₂, ⋯).

^§For most of the MSGs, the set of physical BS fillings {ν}_BS and the set of AI fillings {ν}_AI agree with each other, and they take the form . The superscript letter a indicates violation to this rule, as detailed in table S8.