Table 1 Characterization of BSs in a MSG (excerpt from tables S1 to S6).
MSG*dXBSνBS§
2.4I9(2, 2, 2, 4)1
2.7IV5(2)2
3.4IV3(2)2
209.51IV3(1)2a

*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 Embedded Image, 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 Embedded Image. The superscript letter a indicates violation to this rule, as detailed in table S8.