# Martin Levin

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 retired.

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.

Beginning with a dodecahedron, presented here in silver, and stringing across, creates an icosahedron on the inside, shown here in gold. Conversely, one can begin with an icosahedron and extend its edges to create the dodecahedron outside of it. There is a polarity between the two figures. Each vertex of one is directly above or below a face of the other, and each edge of one crosses an edge of the other. The ratio of the mid-diameters of the dodecahedron to the icosahedron is the square of the golden mean.