Because The LEGO Company get paranoid about this sort of thing I suppose I'd better make it clear that I have no formal affiliation with them, that my views are my own and do not necessarily represent theirs, and so on. So if you think any of this is official you are as deluded as they are.
Another minimal surface - this one was very fiddly and in fact I had to cheat a little bit by using a few plates to hold it all together. But there are only about half a dozen of them - the rest are standard rectangular pieces as usual. And as usual the whole procedure used an unreasonably large proportion of 1x3 bricks (and in this case, 2x3's too).
I chose a slightly non-standard parametrization which tilts the surface because I thought it looked nice balancing on one edge.
Here's a link to an animated GIF of the Costa Surface rotating. Be warned that the file is quite large (about 500K)
As with most of my mathematical surfaces, I made use of some computer assistance. Just in case anyone's interested, here's the raw LDRAW .DAT file generated by my program for this sculpture. Beware - the .DAT file builds it out of 1x1 bricks. Actually constructing this out of larger bricks so that it holds together is a (non-trivial) exercise for the reader!
The Costa surface was the first known non-periodic example of a complete minimal surface without self-intersections. It was first described in 1982 by the Brazilian mathematician Celso Costa. It's a bit tricky getting your head around what the holes are doing. My favourite way of visualising it is to make "V" shapes with the first and second fingers of each hand and then slot the two "V"s into each other. I hope that makes sense.
Here are some links to pages related to the Costa surface:
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This page last modified 1st April 2005