Closed quasigeodesics on the dodecahedron (https://www.quantamagazine.org/mathematicians-report-new-discovery-about-the-dodecahedron-20200831/), paths that start at a vertex and go straight across each edge until coming back to the same vertex from the other side. Original paper: https://arxiv.org/abs/1811.04131, https://doi.org/10.1080/10586458.2020.1712564
I saw this on Numberphile a few months back (video linked in article) but now it's on _Quanta_.
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