The hypercube journey.

I saw the advert in the Birmingham Mail. There was to be an architect and builder exhibition at the Exhibition Centre in six months time. I sent off for full details thinking this might be just what I needed to get my architectural practice out of the doldrums of designing self build homes, specifying and designing sun rooms for already oversized family homes and doing sub contracted work at cost drawings for the little box house builders, squeezing more and more people into less and less space.

The exhibition was to be in two sections – one for architects and one for builders. These were called ‘Architex’ and ‘Buildex’ respectively and somewhat predictably. I see myself as a creative designer, specialising in living spaces’ as it says on my promotional literature so I sent off for the relevant exhibitor forms. I don’t somehow think of myself as a brick on brick builder.

When I got the forms back, I got to work on what I do best. Thinking of and designing a stand that would showcase my abilities. The only problem was the cost. The size of stand that I wanted / needed would more likely put me out of business before I could start designing for my many new clients that I hoped to attract.

I had to think of another way, one that I could achieve at a much lower cost. So it was back to the figurative drawing board – AutoCAD – Revit 2D and 3D, in this case. I had been using AutoCAD since I was at Sussex Uni so it made sense to carry on with it. It was familiar to me, I knew its capabilities and shortcuts and, more important, I knew its limitations.

I started doing what I usually do at the start of a project – doodling while I waited for inspiration to strike.

I drew a front door – always useful to have some sort of portal to your world. Then I started thinking and playing with the 2D/3D possibilities of the software. I started wondering why there was only two dimension schemes in use. We now know the others are all around us – some scientists say that there are at least eleven. Where are they? They are here, we just cannot see them. Try this exercise. You can draw in two dimensions and represent three. One is a dot, two is a line, three is an object but what is four? OK so think of a cube. That’s an object so it must be 3D. Go down one and you have a square. It’s made of lines so it must be 2D. Go back up to the cube and add one dimension – you get a tesseract. This is made from eight cubes but the magic of it is that it only takes up the 3D volume of one cube. It can also be drawn on the AutoCAD in 2D. A tesseract has six times as much internal space as external volume as the 4th dimension does not exist in our physical universe even though the CAD software could draw a 2D/3D wireframe representation of one. I was then conceited enough to think that, if the CAD system could draw it, I could design and build it.

I asked my mate Phil down to the pub for a drink that evening and put the problem to him. He is not one of those people who designs things on the back of an envelope, he just sat there with a dreamy look on his face for about half an hour while I kept him supplied with pints of the local real ale. After a long period of silence he said, ‘to achieve the best volume in 3D it would have to be an unfolded tesseract.’

tesseract-unfolded                                     schlegel_wireframe_8-cell

An unfolded tesseract                                              A folded tesseract

‘How do you mean,’ I asked.

‘Well, if you drop a dimension and then ask the same question, you can cover the greatest surface are by unfolding a cube. If you do that, you get six squares. If you unfold a tesseract you get eight cubes.’

We batted it to and fro for another hour and then we had a decision. I would order a square space in the exhibition hall. This would only be the standard size of one unit, which is 4 metres square. I would then design and build a cube on it which would have sides each of 4 metres. This cube would be built from wood with one door so that no passer-by could see what was in it. Inside the cube I would build an unfolded tesseract to give me an extra seven cubes that could only be seen from the inside of the base cube. This would give me plenty of space to showcase my designs and still leave space for a conference room and a kitchen.

The first day of the exhibition setting up week came and all my materials necessary to build my stand started arriving at the exhibition hall. There were a few startled faces when people saw how many materials were taken into through the front door of my cube. ‘It must be getting very crowded in there,’ was the general reaction. I ignored them and urged my building contractor to continue with the work as quickly as possible – there was a lot of work involved in fitting out the eight cubes.

It was time for the exhibition to open. I stood just outside my cube inviting people in through the door to see my showcased work. It was difficult at first because potential customers assumed that I couldn’t show them much in the space available but the ones that I persuaded to come in were very impressed by the scope of my work and how much space I ‘appeared to have created from nowhere.’ By the second day, the news had spread by word of mouth so the number of visitors to my stand increased rapidly and I was rushed off my feet explaining what I could achieve and then taking and scheduling orders. My stand became the place to be.

The exhibition was to last for five days then the weekend would be taken up by taking down the stands, ready for the packaging exhibition, Packex, the following week.

For me, each day was busier than the day before so, by Friday midday it was getting manic with even the eight cubes in my hypercube getting crowded. The climax came at 1337. My entry counter showed that there were more people in my stand than ever before.

There was suddenly a very loud ‘Snap’. Nearby exhibitors were worried that something dangerous had happened to my stand but no, it was still there and looked entirely undamaged.

It was very different inside. The severe weight loading caused by so many people had caused the tesseract to fold back into itself. Of all the forms it could have ‘chosen’ it had formed itself into the most material and energy efficient form so people were in some very strange shaped spaces.

Luckily, I was quite close to the front door when it happened. The exhibition hall fire and rescue team arrived very quickly and stood there, amazed, while many more people than seem possible slowly walked, unharmed apart from minor shock, out of the front door.

No news of this reached the papers as the exhibition hall owners didn’t want any negative publicity. I was too busy designing buildings for my new customers and none of them were willing to talk about it – who would believe them? It will take me nearly four years to do all the work that flowed from that exhibition and I am now making plans to exhibit at the next one – luckily they are only held every four years – just like the world cup and the olympics.

I am now busy getting the design ready for my new exhibition stand. I have been talking to Phil about the possibility of designing and building a 5 dimensional hypercube…

© Richard Kefford                                                                                                        Eorðdraca

*****

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