I received a Ph.D. in mathematics from Johns Hopkins. For most of my
career I taught high school math in Waldorf schools, where the
pedagogy encourages the bridging of mathematics and art. I'm now
The Platonic solids are quite simple geometric forms, and yet, as one contemplates them and builds up and holds the forms in one’s imagination, they become quite captivating. The center point has a polar plane (in the sense of projective geometry), which is the plane at infinity. One can imagine the form carved out by planes and lines coming in from the infinitely distant periphery. The model shown here is designed to suggest shapes that are not solid blocks, but rather created by lines and planes coming from the periphery.
All five Platonic solids are shown here in relation to one another. The ones with triangular faces, namely the tetrahedron, octahedron, and icosahedron, all share common face planes, while the ones with triangular vertices, namely the tetrahedron, cube, and dodecahedron, all share common vertices. The model shows clearly that all of the symmetries of the tetrahedron are also symmetries of the other four Platonic solids.