Crown multiplications and a higher order Hopf construction

We describe a ternary function (multiplication) σ : S 12 × S 12 × S 12 → S 4 from the product of three 12-point crowns into a 4-point crown in the category of partially ordered sets. The ternary map illustrates a version, in the context of posets, of associative multiplication. A higher order analogue of Hopfʹs construction applied to σ yields a poset model of a certain homotopy class, which we identify, in π 5 ( S 3 ) .