Mathematicians Finally Answer 2,000-Year-Old Question About Dodecahedrons

NCamero (Slashdot reader #35,481) brings some news from the world of 12-sided dodecahedrons:

Quanta magazine reports that a trio of mathematicians has resolved one of the most basic questions about the dodecahedron. The cube, tetrahedron, octahedron and icosahedron cannot have a straight path you could take [starting from a corner] that would eventually return you to your starting point without passing through any of the other corners. The dodecahedron can.

Mathematicians studied dodecahedrons for over 2,000 years without solving the problem, reports Quanta magazine. But now...
Jayadev Athreya, David Aulicino and Patrick Hooper have shown that an infinite number of such paths do in fact exist on the dodecahedron. Their paper, published in May in Experimental Mathematics, shows that these paths can be divided into 31 natural families. The solution required modern techniques and computer algorithms.

"Twenty years ago, [this question] was absolutely out of reach; 10 years ago it would require an enormous effort of writing all necessary software, so only now all the factors came together," wrote Anton Zorich, of the Institute of Mathematics of Jussieu in Paris, in an email.

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