Left-invariant almost nearly K\"ahler structures on $SU(2)\times SU(2)$   in the tetrahedron visualization for $CP^3$
  The set of maximal non-integrable structures $(SU(2)\times SU(2),B,I)$, where $B$ is Killing-Cartan metric is described as subset of $\mathbb{CP}^3$. The visualization of complex projective space $\mathbb{CP}^3$ as tetrahedron which edges and faces are $\mathbb{CP}^1$ and $\mathbb{CP}^2$ is used. 
Natalia Daurtseva