Mathematicians Make New Discovery About the Dodecahedron

Like a lot of kids, I learned about dodecahedrons from The Phantom Tollbooth. In the book, Milo and the watchdog Tock have this exchange with the mathematical object:

The Dodecahedron:
My sides are many, my angles aren’t few. I’m the Dodecahedron, and who are you?

Milo:
What’s a dodecahedron?

Tock:
If I remember correctly, a dodecahedron is a geometrical shape with twelve sides.

As it turns out, mathematicians also really like dodecahedrons, so much so that they’ve made a new discovery that adds to a field of study about geometrical objects that goes back to Plato. Here’s more from MOTHERBOARD:

In a recent paper, mathematicians Jayadev Athreya, David Aulicino, and Patrick Hooper showed that there are 31 kinds of straight paths that begin at a corner of a dodecahedron and walk around the entire shape without touching another corner. Such paths are not possible for any other Platonic solid. An article in Quanta first reported the group’s discovery, which was published in the journal Experimental Mathematics in May.

Aulicino, a mathematics professor with appointments at Brooklyn College and CUNY Graduate Center, said that the group was inspired by two recent papers demonstrating that a straight path starting at a corner and bypassing every other corner could not be made for tetrahedra, cubes, octahedra, and icosahedra. They then adapted an algorithm to answer the straight path question for the dodecahedron.

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