Cubic rational-map ansatz for four Skyrmions ($R(z)=\frac{z^4+2\sqrt{3}i{z}^2+1}{z^4-2\sqrt{3}i{z}^2+1}$)

This degree-four rational map obeys $R(iz)=1/R(z)$ and $R((iz+1)/(1-iz))=e^{2\pi i/3}R(z)$. These pair the generators of the rotational symmetry group of a cube with target rotations, giving combined spatial-isospin symmetry in the Skyrme model. Its spatial half-turn kernel is a Klein four-group. The map gives a cubic four-Skyrmion approximation; preserving only its Wronskian zero set does not guarantee the same rotational symmetry.