A trio of mathematicians have resolved one of the most basic question about Dodecahedron - is there some straight path you could take that would eventually return you to your starting point without passing through any of the other corners?
Jayadev Athreya, Patrick Hooper and David Aulicino have shown that an infinite number of such paths do in fact exist on the dodecahedron.
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https://www.quantamagazine.org/mathematicians-report-new-discovery-about-the-dodecahedron-20200831/
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Mrs.Achala Verma
President
Very helpful ma'am