Toroidal two-Skyrmion ($B=2$)

The standard low-energy $B=2$ Skyrmion in the ordinary Skyrme model has a toroidal baryon-density shape, with axial density symmetry $D_{\infty h}$. Its proper combined field symmetries have an $O(2)$-type stabilizer. The angular ansatz $R(z)=z^2$ in the rational map approximation for Skyrmions explains the axial relation $R(e^{i\theta }z)=e^{2i\theta }R(z)$: spatial rotation through $\theta$ is accompanied by isorotation through $2\theta$. The angular density vanishes at the two axial directions, yielding the toroidal hole. This describes the familiar minimal branch and a useful approximate field; it is not an assertion that every degree-two field is toroidal.