From Magnetic Gears to Halbach Spheres

                                                                                   Talk presented at

Universität des Saarlandes, Physikalisches Kolloquium der Naturwissenschaftlich-Technischen Fakultät. May 7, 2026:

Using spherical neodymium magnets together with open-source graphical user interfaces, this talk presents four intriguing insights into dipole clusters:

1. Eight interacting dipoles exhibit fewer than 16 million equilibria.
2. Two dipoles realize two different cogging-free magnetic gears.
3. Seven dipoles form a “catastrophe machine” illustrating tipping points.
4. Icosahedral symmetry of dipole clusters is not just cool anymore.