Dodecahedrons Just Can't Stay Platonic

2020

 

If you make a solid a celebrity, you have to expect trouble.

 

Plato and other ancient geometers found that only five solid forms have all faces that are equal, regular, and possess equal angles between them. The five are celebrated in geometry as the Platonic Solids. Plato associated four of these special solids (tetrahedrons, cubes, octahedrons, and icosahedrons) with the then-recognized four worldly elements: fire, earth, air, and water. But the dodecahedrons stumped the old philosopher, and he finally gave them an obscure reference to the shape of constellations, thus setting the stage for trouble.

 

To make matters worse, Plato demanded that geometric figures originate in a realm of perfection, and that our worldly representations of them must all be imperfect. Of course, propriety demands that their relationships must remain Platonic.

 

When in our world, wild dodecahedrons cast off perfection with abandon. Conservative geometers label them as dodecadent and don’t let their younger children see the way they relate in public. Nevertheless, we as adults can watch them dance, admiring their freedom to face the world, together in motion.