Each mode's symmetry is denoted as dI, it has a degeneracy d, and transforms as an irrep I of the Skyrmion's symmetry group. We use the notation of Cotton. Character tables may be found here.
The zero modes are translations, rotations and isorotations. These decompose as 3T1, 3T2 and 3T2 respectively.
| Freq. | Symmetry | Description/Notes | Visualization |
|---|---|---|---|
| 0.43 | 3T2 | A vertex of the tetrahedron moves away from its opposing face. Asymptotically, these become separate B=1 and B=2 clusters. |
|
| 0.56 | 2E | Two opposite edges of the tetrahedron pull away from each other, deforming it into a pretzel-like shape. This space contains the well-known twisted-line scattering. |
|
| 0.91 | 3T2 | One vertex grows while the other three shrink. |
|
| 0.94 | 1A1 | The breathing mode. |
|
| 1.01 | 2E | Two vertices isorotate out of phase with the other two. |
|
| 1.59 | 1A2 | Each vertex isorotates about the color on its tip. |
|
Notes
Hover over an image (or if you're on a tablet/phone: tap on an image) to make it come to life. The hover-over text tells you the Cartesian realization of the element of the irrep you are looking at.