This is a model of a mathematical structure called a “Cantitruncated 600-cell”, colloquially known as a 4D buckyball. It took twenty people five hours to build and contains over 10,000 pieces of specialised plastic called Zometool. Such a model has never been seen in the UK before and I’m incredibly proud to have been able to organise its creation in Edinburgh last week.

The sculpture perches at the top of the main staircase in Summerhall, a great arts venue which used to be the University of Edinburgh’s veterinary school. The hall in which we put together those pieces of plastic was no doubt designed for dissecting cows or lecturing students about the removal of dogs’ testicles. Instead, Monday’s event (held as part of the University’s Innovative Learning Week) led our students into looking at the anatomy of geometry and playing with very different sorts of balls.

So what *is* a “Cantitruncated 600-cell”? The description on Wikipedia is less than enlightening. (It does, however, give some other cool names for this shape, including the “**Cantitruncated polydodecahedron**” and “**Great rhombated hexacosichoron**“.) Basically, the 600-cell is a shape made up of 600 tetrahedra (which in turn are 3D shapes made of 4 equilateral triangles) joined so that 20 of them meet at each corner. To ‘truncate’ means to ‘chop off the corners’. If we chop off a corner of the 600-cell, we see a shape which has 20 triangular sides – this is another regular 3D shape called an icosahedron.

‘Cantitruncation’ means ‘truncate, then truncate again’. Truncating the icosahedron leaves us with a shape colloquially known as a buckyball, or football (see left). Putting these facts together, we see that our model is a 4D shape made of 600 tetrahedra, but where each corner has been chopped off and replaced by a buckyball.

I have written a lengthier and much better explanation of this for the School of Mathematics website so recommend that you read that for more details! Otherwise just let your brain gently simmer in the crazy complexities of 4-dimensional geometry.

Photographer (and mathematician) Graeme Taylor was there on the day to do time-lapse photography of the build, and you can watch his final video at:

You can also see photos on Flickr by the University’s photographer Dong Ning Deng (scroll right for more!). Our students had to work very hard to not only put this giant jigsaw together, but also to cope with the engineering challenge of building enough of a framework to not let the model collapse under its own weight. I have to say that the sound of cracking plastic haunted my dreams for some nights afterwards…

Our 4D buckyball will stay in Summerhall until the end of the Edinburgh International Science Festival (20 April) and will (hopefully!) form part of the festival’s Art Trail. So go and see it while it’s there and tell me what you think of it!