# Martin Levin

retired high school math teacher
Portland, Oregon, USA

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.

Cube Inscribed On The Faces Of A Dodecahedron
45 x 45 x 45 cm
brass & aluminum tubing and 3D printed steel joints
2016

A cube inscribed on the regular dodecahedron, with each of its 12 edges on one of the 12 faces of the dodecahedron, was used by Euclid to prove the existence of the regular dodecahedron. This model shows a second way of inscribing the cube on the dodecahedron, with each edge on a face of the dodecahedron. This is done with a larger cube and the dodecahedron faces extended. This second way seems to have not been noticed before. Each edge of the dodecahedron meets two edges of the cube, thereby suspending the dodecahedron inside the cube. Each pentagonal face of the dodecahedron lies on one edge of the cube; its 5 edges meet the one edge of the cube, at the 2 internal and 2 external golden mean points and the point at infinity.