Plastic Zagier Tetrahedron, Figure 3

During a visit with Don Zagier at the Max Planck Institute for Mathematics in Bonn, Germany, June 27-28, the sculptor learned abouth Zagier's recent work involving the unexpected symmetries of a modified (inflated) tetrahedron-like surface given by the equation x2 + y2 + z2 - 2xyz = 1. This equation was the basis for this piece.


A 3D-printed hollow tetrahedron made of plastic. For each value of z, the cross section is an ellipse, which becomes more excentric as z goes to the upper and lower limits. At those limits, the ellipse degenerates to a line segment, making two of the edges of an ideal tetrahedron which sits inside the surface. The length of that line segment, which is the widest the sculpture gets at the top and and the bottom, is 14mm = 5.5". The cross section when z = 0, the middle of the piece, is a circle whose diameter is 10mm.