Martin Levin

retired
Silver Spring, MD, USA

I received a Ph.D. in mathematics from Johns Hopkins. For most of my career I taught high school mathematics in Waldorf schools, where the pedagogy encourages the bridging of mathematics and art. I'm now retired.
The Platonic solids are, in a way, 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. One can view a cube, for instance, as a bounded solid, but it is more than that. The center point of the figure has a dual (in the sense of projective geometry), which is the plane at infinity. Opposite vertices have a common line that lies on the center point, while opposite faces have a common line that lies on the plane at infinity. One can imagine the form carved out by planes and lines coming in from the infinitely distant periphery. The models shown here are designed to suggest shapes that are not solid blocks, but rather created by lines and planes coming from the periphery.

Dodecahedron with Icosahedron Suspended Inside
13" x 13" x 13"
brass and aluminum tubing and steel wire
2008

There is a polarity of space that pairs the vertices of the icosahedron with the faces of the dodecahedron and vice versa; it leaves invariant a sphere that lies between them. The ratio of the mid-radius (i.e. to the midpoint of an edge) of the dodecahedron to the mid-radius of the icosahedron is the golden mean squared.

Icosahedron with Dodecahedron Suspended Inside
10.5" x 10.5" x 10.5"
brass and aluminum tubing and steel wire
2001

The ratio of the mid-radius of the icosahedron to the mid-radius of the dodecahedron is the golden mean.

Relations Between Some Platonic Solids - A Series of Five Models
48" x 48" x 18"