Using a recently established band representation analysis, we discover two distinct types of topological nodal magnons in the real-space antiferroic ordering of whirling spin arrangements in the Tb-based icosahedral quasicrystal 1/1 approximants, both of which originate from a composite band (co)representation $A\uparrow P_{I}n\overline{3}\left(24\right)$ and its constituent elementary band representations. The first type is doubly degenerate nodal line network and nodal planes associated with two-dimensional irreducible band representation, while the second type is a nodal line network due to accidental band inversions. Since our analysis, which relies solely on magnetocrystalline symmetry, is valid for a wide range of materials and spin textures belonging to the same magnetic space group irrespective of composition, these findings offer universal insights into the research of Tb-based quasicrystal approximants as well as a contribution to broadening the range of topological magnon-hosting materials.

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• Magnons
• Spin dynamics
• Quasicrystals
• Topology