Fun Fact of the Week! Shapes Aren’t Just for Kids

Here’s a compendium of some of the many shapes that you never learned in elementary school, and strange facts associated with them. 

Level I: Truncated Icosahedron

Soccer balls are pretty cool and all, but they’ll be even cooler now that you know that the pattern of white hexagons and black pentagons is called a truncated icosahedron.

It’s made via taking an icosahedron (D20, for my D&D enjoyers, or 20 triangles stuck together like a low-res ball for the computer graphics individuals), and performing the geometric equivalent of a circumcision. Each tip (vertex) is flattened away until there is nothing but hexagons and pentagons left. 

Level II: The Platonic Solids

This Power Rangers-esq quintuplet of solids is named for the Big P himself, Plato (although he probably didn’t discover them). The tetrahedron (4 triangles), cube (6 squares), octahedron (8 triangles), dodecahedron (12 pentagons), and icosahedron (20 triangles). Plato also assigned them an element each; fire, earth, air, NA, and water, respectively. Tragically, the dodecahedron never got its own element, but the ether proposed by Aristotle seems a pretty good fit. 

Kepler was interested in the Platonic solids and came up with two more regular polyhedra in 1619. Although they do self-intersect and are non-convex, they look badass, so I’ll give them a pass. Kepler even proposed that each of the 5 known planets at the time was set upon a celestial Platonic solid, which was nested inside of each other and rotated to give the planets motion. It may sound a little crazy, but, to be fair, his mother was tried as a witch over a period of many years, and he did integral calculus on orbital mechanics before Newton knew what a derivative was, so give him some credit. 

Level III: The Trefoil Knot

Knot theory is a branch of mathematics concerned with all of the ways closed 1D loops can exist and ‘get twisty.’ Within knot theory, the Trefoil is the simplest non-trivial knot and is an excellent illustration of how pretty shapes can be. I won’t try to describe it here, as it’s a somewhat complicated shape, but its symmetry makes it an excellent artistic subject. The Celts went wild with them back in the Middle Ages, and if you’re interested in art, come to Paleography Scriptorium in the Trillium Classroom on Thursdays at 6:00pm. 

Level IV: Mucube

The mucube is technically a ‘convex uniform honeycomb’ whatever that means. What the mucube actually is, however, is a cube with two opposite faces removed, and then duplicated and rotated in 3D space, so that it forms an infinite lattice. This is still technically a regular polyhedron (it follows the same rules as the Platonic solids, in that all of the faces are regular, and any face can be moved to cover any other face), but this time, it’s infinite! There are two other shapes like this, which are called Petrie-Coxeter polyhedra, but I chose the mucube because it has the funniest name. 

I would recommend watching the lovely video by YouTuber Jan Misali, entitled ‘there are 48 regular polyhedra’ if you are interested in this shape, the 47 others like it, and ‘dark geometry.’