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

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