This week I’ll be writing about the Platonic Solids. I hesitated about writing this post because there is SO much information already out there about this well-known group of polyhedra. However, I think I also have some new and interesting insights about their potential role as a springboard for geomatric art. So, after a very brief introduction / tour / refresher for those who may not know a much about them, I’ll be focusing on that aspect. I’ll be sure to provide a few links along the way for those who want to learn more about the details and characteristics of the solids themselves.
What Are The Platonic Solids?
The platonic solids are a group of five polyhedra that share a special quality – they are the only five polyhedra whose faces are all the same, regular polygon. In other words, if you start with regular (meaning equal-sided, equal-angled) polygons — equilateral triangle, square, regular pentagon, regular hexagon, etc. — and only use one kind at a time, there are only five polyhedra you can make. Without further ado, here they are:
If you want to read all about their various properties, here are a couple of good links that cover a lot of ground:
OK, So… Why Should I Care?
While these shapes are mathematically and historically important, they don’t immediately leap out as having the potential for art. In and of themselves, they are relatively plain and simple — or, so it would seem. However, if one studies them, one soon realizes that there is a lot more there than meets the eye…
Some Examples of Platonic Solid-Inspired Art
It should come as no surprise that M.C. Escher found a way to take the humble solids and elevate them to art. He was fascinated by, and incorporated, more complex polyhedra as well, but even these simplest of polyhedra played prominent roles. For example, he transformed the simple tetrahedron into a world with four different “ups”:
and he took the fact the the tetrahedron is its own dual (see links above for the definition of duals), and made two dual tetrahedra into contrasting, interlocking worlds:
And, by connecting vertices of the dodecahedron into inner tetrahedra, he formed the framework for this beautiful flower sculpture (one of his few three-dimensional works):
Have You Seen Any Platonic Solid Art?
As you can see, these humble shapes can be springboards for wonderful art. Now that you recognize them, as there other art out there that you recognize as coming from one of these five shapes? If so, let us know in the comments below!