# 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 has a dual (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.

Five regular tetrahedra, each made of brass tubing, are held in tension to one another by steel wires and by black strings. The wires form a circumscribed dodecahedron, while the strings have suspended on them aluminum tubes that form an icosahedron. Unlike a construction of this compound of five tetrahedra that is made with solid faces of paper or wood, here one can see the icosahedron at the core, which is the intersection of the five tetrahedra and the dual of the outer dodecahedron.

Each cube, in string, is inscribed in a brass dodecahedron, vertex on vertex, and in turn has a smaller brass dodecahedron inscribed in it, edge on face. The sizes progress by the golden mean ratio. Four dodecahedra and three intermediate cubes are shown, but one can imagine the progression continuing further outward and further inward indefinitely.