Mathematicians Report New Discovery about the Dodecahedron

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Mathematicians Report New Discovery About the Dodecahedron:

Even though mathematicians have spent over 2,000 years dissecting the structure of the five Platonic solids-the tetrahedron, cube, octahedron, icosahedron, and dodecahedron-there's still a lot we don't know about them.

Now a trio of mathematicians has resolved one of the most basic questions about the dodecahedron.

Suppose you stand at one of the corners of a Platonic solid. 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? For the four Platonic solids built out of squares or equilateral triangles-the cube, tetrahedron, octahedron, and icosahedron-mathematicians recentlyfigured out that the answer is no. Any straight path starting from a corner will either hit another corner or wind around forever without returning home. But with the dodecahedron, which is formed from 12 pentagons, mathematicians didn't know what to expect.

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.

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