This paper investigates several distinct attempts to generalize in higher dimension the standard 2-dimensional phyllotaxy set construction. We first recall known constructions for these sets on 2D manifolds of constant curvature (the Euclidean plane \(\mathbb {R}^2\) , the sphere \(\mathbb {S}^2\) and the hyperbolic plane \(\mathbb {H}^2\) ). We then propose a first attempt to get a 3D phyllotactic set by piling up suitably shifted Euclidean 2D phyllotactic sets. A different, radially triggered, solution is then analyzed. An interesting phyllotactic set on the hypersphere \(\mathbb {S}^3\) is then generated using a Hopf fibration approach. Finally, a simple 4-dimensional example is presented, generated as a simple product of two 2-dimensional planar sets. A 3D phyllotaxy candidate is then derived by applying a “Cut and Project” algorithm.
