Crown multiplications and a higher order Hopf construction (Q886298)

This is a short but very interesting paper. The authors describe a ternary function (multiplication) \(\sigma: \mathbb{S}_{12}\times \mathbb{S}_{12}\times\mathbb{S}_{12}\to \mathbb{S}_4\) from the product of three \(12\)-point crowns into a \(4\)-point crown in the category of partially ordered set. By applying a higher-order form of Hopf's construction to \(\sigma\), the nontrivial element in \(\pi_5(S^3)=\mathbb{Z}/2\) is then obtained.