# What math object is the wire star on Will Hunting's prof's desk?

Just after Will Hunting has dumped his girlfriend, the professor enters his office to meet Will which ends with Will offending him too, setting his own research solution on fire and calling it a waste of time.

On the desk is a wire model. Watching right from the start of the scene at about 1h23", you can see it in motion. It seems to consist of three crosses sharing a centerpoint and rotated in space, but I can't quite put it before my mind's eye. It's in the right-hand foreground in the still below.

What's the name and meaning of that mathematical object, or the solid it spans?

• I suppose some might think this belongs on Math.SE, but it would be nicer to have it here if the knowledge is around. Commented Jun 4 at 15:51

The prop was made by KO Sticks. You can see some set photos with the wire star.

In 1997, a Six-Axis Star made its way to being a prominent prop on the MIT math professor's desk in the movie Good Will Hunting:

The site's owner explains, in considerable detail, how these objects were formed mathematically and what they represent in terms of folded space.

A few years later, I began to do just this, starting with building models of some of the structures I had learned from Fuller. Of particular interest was a concept that he called Tensegrity, which is attributed to Kenneth Snelson. In these models, struts, or sticks, are suspended from each other by a network of tension members, such as strings, or wires. The sticks do not collide or intersect, but are coupled together by tension as they pass by each other. Thus symmetry and structural integrity are resultants of the assemblage of simple linear components, tension and compression, push and pull. The sparsity of this kind of definition of spatial form was very appealing to me.

The basic idea, the story of the stars, is that I found it inspiring that one could build objects that are mathematically elegant and have structural integrity, working with simple, readily available components, and using basic tools and techniques. These wire sculptures are stable, yet flexible, expressions of spatial symmetry that do not require any precision machining, casting, etc. The intent was, and still is, to make the geometry and physics that are expressed through the stars accessible and appealing. They are a kind of fusion of science and art.

• In that still you can also see models of the compound of five octahedra and the compound of five cubes (which are dual to one another and both discovered by Edmund Hess). Commented Jun 5 at 8:47
• The same website provides some clearer photos of the object. The photo with the purple background provides the most detailed view of the structure. A symmetric polyhedron that crudely approximates the object can be constructed by attaching an elongated pyramid with pentagonal base to each of the pentagonal faces of a regular dodecahedron. Commented Jun 5 at 14:57
• Tensegrity is cool, and those are some nice specimens. Thanks. Commented Jun 5 at 17:14
• @WillOrrick Nice. It should be easily doable with SketchUp for example. Add a small twist to the pyramid, and it would look great already Commented Jun 6 at 14:36