Fig. 4: Two distinct groups of octupolar ground states on an icosahedron for antiferromagnetic Jzz based on the symmetry ground.
From: Unveiling multipole physics and frustration of icosahedral magnetic quasicrystals
a 60 degenerate states with no 5-fold rotational symmetry. b 12 degenerate states with 5-fold symmetry. Z-axis is the 5-fold rotational symmetry axis in (b). c, d Top view along Z-axis in (a, b), respectively. (c) Mirror reflection with respect to σ plane containing Z-axis swaps the octupoles on the sites Q and R. This leads to another degenerate state which lacks the 5-fold symmetry. d The state depicted in (b) possesses 5-fold rotational symmetry along Z-axis.
