Hyperbolic Paraboloid

I have seen some activities that used skewers to create hyperbolic paraboloid surfaces. I thought I'd experiment with something similar, perhaps to use in a workshop setting with students. I went for a similar structure but used wool instead of skewers.

I created the tetrahedral frame from 6 skewers and stuck them together using a glue gun. This was possibly not the best idea as it was a bit messy. I then attempted to thread the wool round the skewers. There wasn't enough friction though so I used the glue gun to create dots equidistant along the frame to stop the wool from sliding around. I threaded orange wool one way and yellow wool the other way. 

The lovely geometric property of this shape is that it is a doubly ruled surface. This can be easily seen here by looking at the orange and yellow wool separately. It is one of only 3 surfaces to have this property, the others being the plane and the hyperboloid of one sheet.

This property also means that hyperbolic paraboloids are used to great effect in architecture, often as a sweeping roof structure.

Here are some examples including a church in New Jersey, a car showroom in New York, a petrol station on the A1, a metro station in Warsaw and the velodrome in London.