Saul Schleimer, a mathematician at the University of Warwick, and Henry Segerman, a mathematician at the University of Melbourne, are the co-creators of the Thirty Cell puzzle. They are both theoretical math researchers who also enjoy using 3-D printing—a technique for manufacturing a three-dimensional object from a computer program—to create mathematical art and visualizations. (In August, Scientific American featured some of Segerman’s sculptures in a slide show from the Bridges math-art conference.) This puzzle is a projection of a four-dimensional shape into our three-dimensional world. To explain how the projection was created, Schleimer brings it down a dimension and starts with a three-dimensional cube. Imagine a cube sitting inside a sphere. Now put yourself at the middle, holding a flashlight. The light projects all the edges and vertices out to the surface of the sphere. “We replace the usual cube that we know and love with a roundy cube on the sphere,” says Schleimer. This process is called radial projection.
Segerman and Schleimer use the company Shapeways to print their models. They use programs such as Python, Adobe Illustrator and Rhino to create files of an object that they send to Shapeways to translate into very precise 3-D models. Shapeways uses the computer files to program a laser to fuse powders into the shape of a 3-D object. It can even print objects with multiple interlinked components, such as the the fidget above. Another popular type of 3D printer, MakerBot, melts new layers of a material over previously deposited ones, so the models must be supported during the entire process. Shapeways doesn’t have that constraint, but its printers are more expensive. The company lets people upload their models and then ships the printed material out to them, rather than having users own printers themselves.
Via Dr. Stefan Gruenwald