A complilation of many of the shapes I made while at IHP.

A cloth with normal vectors sticking out. Draping this over a surface, we can visualize its normal field. In this picture, we see the normals to a constant negative curvature surface. For more pictures and information, see my page here

A mechanical device which approximates constant negative curvature surfaces. Made with Chaim Goodman-Strauss and Henry Segerman. For mathematical and constructional details, see my page here

A hyperbolic sculpture, made out of right angled pentagpns. The pentagons were filled with hyperbolic paper to build a surface. Many people at the trimester contributed to this. For more details, see my page here

To quickly make a pseudosphere, build many cones of the same radius but different cone angles. Then, stack them in order of angle. In the limit of many cones, the cross section is a Tractrix, so the result is the surface of revolution of a tractrix. It just so happens that this has constant negative curvature! I learned about this from Fran Herr, who says it goes back to Thurston (like all good things). The innovation here is to not tape the cones together. Instead, snip off their tops, and stack them on a little rod. Then, we can bend the rod this way and that, and have so much fun. For more information, see my page here

A model of the edges of a 24 cell, inflated to lie on $S^3$, then stereographically projected to $\RR^3$. The coloring shows a way of decomposing the 24 cell into 3 disjoint hypercubes. Designed by Chaim Goodman-Strauss, see here. He’s made a large scupture using this design
Photo credit Edmund Harris

A nice curve bent out of a brass tube. This was meant to be the border of a minimal surface, formed by stretching fabric around the tubing. I never got this to work. Still, looks cool.

A woven pentagon-and-square tiling. Made during Alison Martin’s workshop during the geometry conference. See my own exploraitons on paper weaving

Over the semester, the common area got innundated by all the shapes people made at the shape factory. The piano was completly buried. At the end, I couldn’t take many of my objects to americal with me, for they were too large and delicate. Hence, the pile of free stuff.